Multiple Correct Answers MCQs for Sub-Topics of Topic 15: Financial Mathematics

Question 1. Select all correct statements about the concept of Principal in finance.

(A) It is the initial amount borrowed or invested.

(B) It includes the interest earned over time.

(C) It is the base amount on which interest is calculated.

(D) It decreases over time in a simple interest scenario.

(E) It increases over time when interest is added.

Question 2. Which of the following are components of the "Amount" accumulated at the end of an investment period?

(A) Principal

(B) Interest Earned

(C) Time Period

(D) Interest Rate

(E) Taxes Paid

Question 3. Select all correct statements regarding Interest.

(A) It is the reward for lending money.

(B) It is the cost of borrowing money.

(C) It is always a fixed percentage of the principal.

(D) It is the difference between the Amount and the Principal.

(E) It is independent of the time period.

Question 4. Which factors directly influence the total interest earned on a principal amount?

(A) Initial Principal

(B) Interest Rate

(C) Time Period

(D) Inflation Rate

(E) Taxation

Question 5. A periodic interest rate can refer to the rate applied over which of the following periods?

(A) Monthly

(B) Quarterly

(C) Half-yearly

(D) Daily

(E) Annually

Question 6. The concept of Accumulation involves which of the following?

(A) The growth of the initial investment over time.

(B) The value of the investment at a future date.

(C) Adding earned interest to the principal.

(D) Calculating the present value of a future sum.

(E) Deducting expenses from the principal.

Question 7. If you know the Principal and the Amount, which of the following can you determine?

(A) The total interest earned.

(B) The simple interest rate.

(C) The time period of the investment.

(D) Whether simple or compound interest was used.

(E) The accumulation over the period.

Question 8. Which of the following influence the "Amount" accumulated from a principal investment?

(A) The initial principal amount.

(B) The interest rate applied.

(C) The duration of the investment.

(D) The frequency of interest calculation.

(E) The initial investment strategy (e.g., stocks vs. bonds).

Question 9. When comparing different investment options, what aspects of the interest rate are important to consider?

(A) Whether it is an annual or periodic rate.

(B) The nominal rate.

(C) The effective rate.

(D) Whether it is a fixed or variable rate.

(E) The colour of the bank branch.

Question 10. Select all statements that correctly describe the relationship between Principal, Interest, and Amount.

(A) Amount = Principal + Interest

(B) Interest = Amount - Principal

(C) Principal = Amount - Interest

(D) Amount = Principal $\times$ Interest

(E) Interest = Principal / Amount

Question 1. Select all correct formulas for calculating Simple Interest ($I$) where $P$ is Principal, $R$ is annual rate (as a decimal), and $T$ is time in years.

(A) $I = PRT$

(B) $I = \frac{P \times R \times T}{100}$ (where R is percentage rate)

(C) $I = P(1+RT)$

(D) $I = \text{Amount} - P$

(E) $I = P R^T$

Question 2. Which of the following statements are true about Simple Interest?

(A) Interest is calculated only on the initial principal.

(B) The interest earned is constant for each period (assuming constant rate and time unit).

(C) The principal amount on which interest is calculated changes every period.

(D) It is easier to calculate compared to compound interest.

(E) It results in a higher accumulation than compound interest over long periods.

Question 3. If $\textsf{₹}10,000$ is invested at 6% per annum simple interest for 5 years, which of the following statements are correct?

(A) The annual interest earned is $\textsf{₹}600$.

(B) The total simple interest earned is $\textsf{₹}3,000$.

(C) The amount accumulated at the end is $\textsf{₹}13,000$.

(D) The interest earned in the 3rd year is $\textsf{₹}600$.

(E) The interest is compounded annually.

Question 4. The formula for calculating the total Amount ($A$) with Simple Interest ($I$) and Principal ($P$) is given by which of the following?

(A) $A = P + I$

(B) $A = P(1 + RT)$ (where R is annual rate as decimal, T is years)

(C) $A = P + \frac{PRT}{100}$ (where R is annual percentage rate, T is years)

(D) $A = P \times I$

(E) $A = P(RT)$

Question 5. If a sum of money doubles itself in 10 years at simple interest, select all correct statements.

(A) The interest earned equals the principal.

(B) The annual simple interest rate is 10%.

(C) The amount at the end of 5 years is 1.5 times the principal.

(D) It will become four times itself in 20 years.

(E) It will become triple itself in 15 years.

Question 6. Which of the following scenarios are typically calculated using Simple Interest?

(A) Short-term loans (often less than a year).

(B) Certain types of government bonds.

(C) Savings accounts where interest is credited periodically and compounds.

(D) Loans where EMIs are calculated.

(E) Calculations involving daily interest on overdue payments (if interest doesn't add to principal daily).

Question 7. If the simple interest on $\textsf{₹}5,000$ for $X$ years at 6% p.a. is $\textsf{₹}1,200$, which of the following are true?

(A) $X = \frac{1200 \times 100}{5000 \times 6}$

(B) $X = 4$ years

(C) The amount after $X$ years is $\textsf{₹}6,200$.

(D) The annual interest is $\textsf{₹}300$.

(E) If the time was 2 years, the interest would be $\textsf{₹}600$.

Question 8. To calculate simple interest when the time is given in months, you should:

(A) Divide the number of months by 12 to convert it to years.

(B) Use the number of months directly as 'T' in the formula $PRT$.

(C) Convert the annual rate to a monthly rate by dividing by 12, and use months for T.

(D) Multiply the number of months by 12.

(E) Ensure the rate and time are in the same units (e.g., both annual or both monthly).

Question 9. If Principal is $\textsf{₹}10,000$, Simple Interest is $\textsf{₹}2,000$, and Time is 4 years, which of the following are correct about the rate?

(A) $I = \frac{PRT}{100}$ applies.

(B) $2000 = \frac{10000 \times R \times 4}{100}$

(C) The annual simple interest rate is 5%.

(D) The rate as a decimal is 0.05.

(E) If the rate was 10%, the interest would be $\textsf{₹}4,000$.

Question 10. The accumulation (amount) under simple interest increases ________ with time, assuming a positive rate.

(A) Exponentially

(B) Linearly

(C) At a decreasing rate

(D) By a constant amount each year

(E) Proportionally to the square of time

Question 1. Which of the following describe the concept of compounding in Compound Interest?

(A) Interest earned in one period becomes part of the principal for the next period.

(B) Interest is calculated on the initial principal plus any accumulated interest.

(C) It leads to earning "interest on interest".

(D) The principal remains constant throughout the investment period.

(E) It applies only to short-term investments.

Question 2. Select all correct formulas for the Amount ($A$) accumulated from a Principal ($P$) invested at an annual rate $r$ (as a decimal) compounded annually for $n$ years.

(A) $A = P(1 + r)^n$

(B) $A = P + P \times r \times n$

(C) $A = P(1 + r/100)^n$ (where r is percentage rate)

(D) $A = P + CI$ (where CI is Compound Interest)

(E) $A = P \times (1 + rn)$

Question 3. If $\textsf{₹}50,000$ is invested at 8% per annum compounded annually for 2 years, which of the following are true?

(A) The amount at the end of year 1 is $\textsf{₹}54,000$.

(B) The interest earned in year 1 is $\textsf{₹}4,000$.

(C) The interest earned in year 2 is calculated on $\textsf{₹}50,000$.

(D) The interest earned in year 2 is $\textsf{₹}4,320$.

(E) The total compound interest for 2 years is $\textsf{₹}8,000$.

Question 4. If interest is compounded $m$ times per year, and the annual nominal rate is $r$ (as a decimal) for $n$ years, the formula for the Amount ($A$) is $A = P(1 + r/m)^{nm}$. Which of the following are correct representations of the periodic rate and total number of periods?

(A) Periodic Rate $= r/m$

(B) Periodic Rate $= r/n$

(C) Total Periods $= n \times m$

(D) Total Periods $= n / m$(E) If compounded quarterly ($m=4$), the periodic rate is $r/4$ and total periods are $4n$.

Question 5. An investment of $\textsf{₹}1,00,000$ is made at 6% per annum compounded semi-annually for 1 year. Which of the following are correct?

(A) The periodic rate is 3%.

(B) The number of compounding periods is 1.

(C) The amount at the end of 1 year is $100000(1 + 0.03)^2$.

(D) The amount at the end of 1 year is $\textsf{₹}1,06,090$.

(E) The compound interest earned is $\textsf{₹}6,090$.

Question 6. Select all true statements about the difference between Simple Interest (SI) and Compound Interest (CI).

(A) For a period of exactly one year, CI is equal to SI (assuming annual compounding).

(B) For a period less than one year, CI is equal to SI (assuming no intra-year compounding for CI).

(C) For a period greater than one year, CI > SI (assuming positive interest rate).

(D) CI is calculated on the reducing balance, while SI is on the original principal.

(E) Simple interest grows faster than compound interest over long periods.

Question 7. If a sum of money triples itself in $n$ years at compound interest (compounded annually), which of the following equations can be used to find the annual rate $r$ (as a decimal)?

(A) $3P = P(1 + r)^n$

(B) $3 = (1 + r)^n$

(C) $r = 3^{1/n} - 1$

(D) $r = (3/P)^{1/n} - 1$

(E) $r = \frac{2}{n}$ (This is true for simple interest, not compound)

Question 8. Which of the following affects the total compound interest earned on an investment?

(A) The initial principal.

(B) The nominal interest rate.

(C) The compounding frequency.

(D) The total investment period.

(E) The investor's age.

Question 9. To calculate the Compound Interest (CI) earned, given the Principal (P) and Accumulated Amount (A), which of the following are correct?

(A) $CI = A - P$

(B) $CI = P(1 + r)^n - P$ (for annual compounding)

(C) $CI = P((1 + r/m)^{nm} - 1)$ (for $m$ compounding periods per year)

(D) $CI = Prn$

(E) $CI = A/P$

Question 10. If interest is compounded more frequently (e.g., monthly vs. annually), for the same nominal annual rate and principal, which of the following are true?

(A) The periodic interest rate is higher.

(B) The total number of compounding periods increases.

(C) The accumulated amount at the end of a year will be higher.

(D) The effective annual rate will be higher.

(E) The total interest earned will be lower.

Question 1. Which of the following statements accurately describe a Nominal Interest Rate?

(A) It is the stated or advertised interest rate.

(B) It does not account for the effects of compounding within a year.

(C) It is usually quoted on an annual basis.

(D) It is the true annual rate earned or paid after accounting for compounding.

(E) It is always lower than the effective rate when compounding is more than once a year.

Question 2. Select all correct statements about the Effective Interest Rate ($r_{eff}$).

(A) It is the actual annual rate of return or cost.

(B) It accounts for the effect of compounding frequency.

(C) It is always equal to the nominal rate.

(D) It is the rate that, if compounded annually, would yield the same result as the nominal rate compounded more frequently.

(E) It helps in comparing investment options with different compounding periods.

Question 3. If the nominal rate is $r_{nom}$ per annum and interest is compounded $m$ times per year, which of the following formulas can be used to calculate the effective annual rate ($r_{eff}$)?

(A) $r_{eff} = (1 + r_{nom}/m)^m - 1$

(B) $r_{eff} = (1 + \text{Periodic Rate})^m - 1$

(C) $r_{eff} = r_{nom}$ (only if $m=1$)

(D) $r_{eff} = r_{nom} \times m$

(E) $r_{eff} = r_{nom} / (1+m)$

Question 4. Which of the following scenarios would require calculating the effective annual rate to make a fair comparison?

(A) Comparing a bank deposit offering 6% compounded monthly with a fixed deposit offering 6.1% compounded annually.

(B) Comparing a loan at 10% simple interest with a loan at 9.8% compounded semi-annually.

(C) Comparing two fixed deposits both offering 7% compounded annually.

(D) Comparing the interest earned on $\textsf{₹}1,000$ and $\textsf{₹}2,000$ at the same interest rate and period.

(E) Comparing two credit card offers with different nominal rates and compounding frequencies.

Question 5. If the nominal rate is 8% per annum compounded quarterly, which of the following are correct?

(A) The periodic rate is 2%.

(B) The number of compounding periods per year is 4.

(C) The effective annual rate is exactly 8%.

(D) The effective annual rate is calculated as $(1 + 0.08/4)^4 - 1$.

(E) The effective annual rate is greater than 8%.

Question 6. Which of the following statements correctly describe the relationship between nominal and effective interest rates?

(A) Effective rate is always greater than the nominal rate when $m > 1$ and $r_{nom} > 0$.

(B) Nominal rate is always greater than the effective rate when $m > 1$ and $r_{nom} > 0$.

(C) Effective rate equals the nominal rate only when $m=1$ (annual compounding).

(D) The difference between the effective and nominal rate increases as the compounding frequency increases.

(E) Simple interest rate is a type of effective rate.

Question 7. The concept of interest rate equivalency is used to find:

(A) A simple interest rate that yields the same accumulation as a given compound interest rate over a specific period.

(B) A compound interest rate with one compounding frequency that yields the same accumulation as another compound interest rate with a different compounding frequency over a specific period.

(C) The principal amount that would generate a certain amount of interest.

(D) The time period required for an investment to reach a specific value.

(E) The nominal rate corresponding to a given effective rate and compounding frequency.

Question 8. If you are told that the effective annual rate on an investment is 7%, what does this mean?

(A) The nominal annual rate is also 7%.

(B) For every $\textsf{₹}100$ invested, you will earn $\textsf{₹}7$ in interest over one year.

(C) The accumulation at the end of one year will be $P \times (1 + 0.07)$.

(D) If the nominal rate was 7% compounded monthly, the effective rate would be higher than 7%.

(E) It is a less reliable measure than the nominal rate.

Question 9. Which of the following are equivalent ways to express an interest rate of 12% per annum compounded monthly?

(A) A periodic rate of 1% per month.

(B) A nominal rate of 12% with $m=12$.

(C) An effective annual rate of $(1 + 0.12/12)^{12} - 1$.

(D) An effective annual rate of 12.68% (approx).

(E) A simple interest rate of 12% per annum over one year.

Question 10. When comparing loan options, focusing on the effective annual rate rather than the nominal rate is beneficial because:

(A) It shows the actual percentage cost of borrowing over a year.

(B) It accounts for the impact of compounding frequency.

(C) It is often mandated by regulations for transparency.

(D) It is always a smaller number than the nominal rate.

(E) It simplifies the calculation of simple interest.

Question 1. Select all correct statements about the Time Value of Money (TVM).

(A) A sum of money today is generally worth more than the same sum in the future.

(B) TVM is based on the concept of interest or rate of return.

(C) TVM is used to compare cash flows occurring at different points in time.

(D) TVM ignores the impact of inflation.

(E) A rupee today has the same value as a rupee tomorrow.

Question 2. Present Value (PV) is:

(A) The value of a future cash flow today.

(B) Calculated by discounting future cash flows back to the present.

(C) Always equal to the future value.

(D) Higher for a higher discount rate.

(E) The principal amount invested today.

Question 3. Future Value (FV) is:

(A) The value of a present cash flow at a future date.

(B) Calculated by compounding a present cash flow forward in time.

(C) Used to project the growth of investments.

(D) Lower for a higher interest rate (assuming positive rate).

(E) The interest earned over time.

Question 4. If $PV$ is the Present Value, $FV$ is the Future Value, $r$ is the interest rate per period (as decimal), and $n$ is the number of periods, select the correct relationships.

(A) $FV = PV \times (1 + r)^n$

(B) $PV = FV / (1 + r)^n$

(C) $PV = FV \times (1 + r)^{-n}$

(D) $FV = PV + Prn$

(E) $PV = FV \times (1 - r)^n$

Question 5. Net Present Value (NPV) is a financial metric used for investment decisions. Select all correct statements about NPV.

(A) NPV = Sum of Present Values of all cash inflows - Sum of Present Values of all cash outflows.

(B) A positive NPV indicates that the project is expected to add value.

(C) If NPV > 0, the project is generally acceptable.

(D) If NPV < 0, the project is expected to destroy value and should be rejected.

(E) NPV equals the initial investment.

Question 6. Which of the following are practical applications of Present Value calculations?

(A) Determining the lump sum needed today to fund a child's future education expenses.

(B) Calculating the fair price of a bond that pays future interest and principal.

(C) Valuing a stream of future rental income.

(D) Estimating how much your retirement savings will grow by a certain age.

(E) Calculating the EMI for a loan.

Question 7. Which of the following are practical applications of Future Value calculations?

(A) Projecting the growth of a fixed deposit over time.

(B) Estimating the value of your current mutual fund investments after several years.

(C) Calculating the target amount needed in a sinking fund.

(D) Determining the present cost of a perpetual stream of income.

(E) Comparing investment options based on their potential future worth.

Question 8. If the required rate of return (discount rate) for a project increases, how does it affect the project's NPV (assuming positive future cash inflows)?

(A) The present value of future cash inflows decreases.

(B) The present value of future cash outflows decreases.

(C) The NPV tends to decrease.

(D) The NPV tends to increase.

(E) It has no effect on NPV.

Question 9. You are offered $\textsf{₹}1,00,000$ today or $\textsf{₹}1,10,000$ in one year. If your required rate of return is 9% per annum, which option(s) should you choose based on TVM principles?

(A) Calculate the PV of $\textsf{₹}1,10,000$ received in one year at 9%.

(B) Calculate the FV of $\textsf{₹}1,00,000$ today at 9% for one year.

(C) Compare the PV of the future sum with $\textsf{₹}1,00,000$.

(D) Compare the FV of the current sum with $\textsf{₹}1,10,000$.

(E) Both options are equally valuable.

Question 10. The discount rate used in PV calculations reflects:

(A) The riskiness of the cash flow.

(B) The time value of money.

(C) The opportunity cost of capital (what could be earned elsewhere).

(D) The rate at which money is compounded.

(E) The nominal interest rate only.

Question 1. Which of the following are characteristics of an Annuity?

(A) A series of payments.

(B) Payments are equal in amount.

(C) Payments are made at fixed intervals.

(D) Payments continue indefinitely.

(E) It involves only a single lump sum.

Question 2. Select all correct statements about an Ordinary Annuity (Regular Annuity).

(A) Payments are made at the beginning of each period.

(B) Payments are made at the end of each period.

(C) Examples include loan repayments (EMIs) or bond interest payments.

(D) The first payment occurs one period from today.

(E) The Future Value calculation compounds the last payment for zero periods.

Question 3. Select all correct statements about an Annuity Due.

(A) Payments are made at the beginning of each period.

(B) Examples include rent payments or insurance premiums.

(C) The first payment occurs immediately (today).

(D) Its Future Value is calculated by compounding the FV of an ordinary annuity for one extra period.

(E) Its Present Value is calculated by discounting the PV of an ordinary annuity for one period.

Question 4. To calculate the Future Value (FV) of an ordinary annuity of annual payments $Pmt$ for $n$ years at annual interest rate $i$, which of the following are part of the calculation logic?

(A) Each payment is compounded forward to the end of the term.

(B) The first payment is compounded for $n-1$ periods.

(C) The last payment is compounded for 1 period.

(D) The sum of the future values of all individual payments is calculated.

(E) The formula $Pmt \times \left[ \frac{(1+i)^n - 1}{i} \right]$ is used.

Question 5. To calculate the Present Value (PV) of an ordinary annuity of annual payments $Pmt$ for $n$ years at annual interest rate $i$, which of the following are part of the calculation logic?

(A) Each payment is discounted back to the present (time 0).

(B) The first payment is discounted for 1 period.

(C) The last payment is discounted for $n-1$ periods.

(D) The sum of the present values of all individual payments is calculated.

(E) The formula $Pmt \times \left[ \frac{1 - (1+i)^{-n}}{i} \right]$ is used.

Question 6. If an annuity has payments occurring more frequently than annually (e.g., monthly payments and annual rate), which adjustments are typically needed for the annuity formulas?

(A) The annual rate should be divided by the number of payment periods per year to get the periodic rate.

(B) The total number of years should be multiplied by the number of payment periods per year to get the total number of periods.

(C) The payment amount must be adjusted proportionally to the frequency.

(D) The nominal annual rate should be used directly in the formula.

(E) The number of periods should be divided by the number of payments per year.

Question 7. You are saving for retirement by depositing $\textsf{₹}5,000$ at the end of each year for $20$ years into an account earning 8% per annum. Which of the following concepts are relevant?

(A) Ordinary Annuity

(B) Future Value of an Annuity

(C) Sinking Fund (as it's about accumulating a future sum)

(D) Present Value of an Annuity

(E) Perpetuity

Question 8. You are evaluating whether you can afford a loan that requires fixed monthly payments for several years. Which of the following concepts are most directly relevant?

(A) Ordinary Annuity (payments at the end of the month)

(B) Present Value of an Annuity (loan amount is the PV of future payments)

(C) EMI Calculation

(D) Future Value of an Annuity

(E) Simple Interest Calculation

Question 9. For the same payment amount, interest rate, and number of periods, which of the following statements are true?

(A) The Future Value of an Annuity Due is greater than the Future Value of an Ordinary Annuity.

(B) The Present Value of an Annuity Due is greater than the Present Value of an Ordinary Annuity.

(C) The Future Value of an Annuity Due equals the FV of Ordinary Annuity multiplied by $(1+i)$.

(D) The Present Value of an Annuity Due equals the PV of Ordinary Annuity multiplied by $(1+i)$.

(E) The timing of payments does not affect the value of the annuity.

Question 10. Which of the following are examples of annuities in a financial context?

(A) Regular pension payments received after retirement.

(B) Fixed monthly rent payments.

(C) Equal monthly installments (EMIs) for a loan.

(D) A single lump-sum inheritance.

(E) Irregular dividends from stocks.

Question 1. Which of the following are characteristics of a Perpetuity?

(A) A series of equal payments.

(B) Payments made at fixed intervals.

(C) Payments continue forever (indefinitely).

(D) It has a finite Present Value (if the interest rate is positive).

(E) It has a finite Future Value.

Question 2. The Present Value (PV) of an ordinary perpetuity with periodic payment $Pmt$ and periodic interest rate $i$ is given by $PV = Pmt/i$. This formula is derived from the PV of an ordinary annuity formula by assuming that:

(A) The number of periods ($n$) approaches infinity ($\lim\limits_{n \to \infty}$).

(B) $(1+i)^{-n}$ approaches 0 as $n \to \infty$ (for $i > 0$).

(C) The payment amount ($Pmt$) approaches infinity.

(D) The interest rate ($i$) approaches 0.

(E) The first payment is immediate.

Question 3. Which of the following are examples or applications of the perpetuity concept?

(A) Valuing preferred stock that pays constant dividends indefinitely.

(B) Estimating the capital required to generate a perpetual stream of income.

(C) Valuing a loan with a fixed number of monthly EMIs.

(D) Certain types of perpetual bonds issued by governments.

(E) Calculating the lump sum needed to pay for college education.

Question 4. What is a Sinking Fund?

(A) A fund where money is deposited regularly.

(B) A fund created to accumulate a specific sum of money by a future date.

(C) A fund used to repay a large debt or replace an asset.

(D) A fund where the principal is depreciated over time.

(E) A fund that provides periodic payments forever.

Question 5. Calculating the required periodic contributions to a sinking fund involves applying the concept of:

(A) Present Value of an Ordinary Annuity.

(B) Future Value of an Ordinary Annuity.

(C) Amortization.

(D) Finding the payment amount ($Pmt$) given a target Future Value ($FV$), interest rate ($i$), and number of periods ($n$).

(E) Simple Interest.

Question 6. A company needs $\textsf{₹}10,00,000$ in $10$ years and plans to create a sinking fund with annual contributions at the end of each year, earning 7% per annum. Which of the following are relevant to calculate the required annual contribution?

(A) The target future value is $\textsf{₹}10,00,000$.

(B) The number of periods is $10$.

(C) The interest rate per period is $7\%$.

(D) The formula for the Future Value of an Ordinary Annuity is used, solved for the payment amount.

(E) The present value of $\textsf{₹}10,00,000$ is needed.

Question 7. If the interest rate available for a sinking fund increases, and the target future value and time period remain the same, which of the following are true about the required periodic contribution?

(A) The required periodic contribution will increase.

(B) The required periodic contribution will decrease.

(C) The total interest earned by the fund will increase.

(D) The number of periods will decrease.

(E) The formula for PV of annuity is used.

Question 8. Which of the following distinguishes a perpetuity from an ordinary annuity?

(A) Perpetuity payments are equal, while annuity payments can vary.

(B) Perpetuity payments continue indefinitely, while annuity payments are for a fixed term.

(C) Perpetuity payments start immediately, while annuity payments start later.

(D) Only perpetuities have a present value.

(E) Perpetuities are a special case of annuities where the number of periods is infinite.

Question 9. A sinking fund is used to save *up* for a future expenditure, while EMIs on a loan are used to pay *down* a current debt. This means:

(A) Sinking fund calculations relate to the Future Value of an Annuity.

(B) EMI calculations relate to the Present Value of an Annuity.

(C) The cash flow direction is opposite (deposits into a sinking fund, payments from borrower for EMI).

(D) Interest earned is added to the fund in a sinking fund, while interest paid is part of the EMI payment.

(E) Both involve simple interest.

Question 10. If you invest $\textsf{₹}10,000$ in a special scheme that promises to pay you $\textsf{₹}800$ annually forever, what is the implied rate of return based on the perpetuity concept?

(A) The present value is $\textsf{₹}10,000$.

(B) The annual payment is $\textsf{₹}800$.

(C) $PV = Pmt/i$ applies, so $10000 = 800/i$.

(D) The implied annual rate of return is 8%.

(E) The implied annual rate of return is 12.5%.

Question 1. Which of the following are true about a typical loan?

(A) A principal amount is provided by the lender to the borrower.

(B) The borrower agrees to repay the principal plus interest.

(C) Repayment is usually done over a specified period.

(D) The total amount repaid is always less than the principal.

(E) It is a form of equity financing.

Question 2. An Equated Monthly Installment (EMI) is designed such that:

(A) The amount of the payment is the same each month.

(B) It covers both the principal and interest components of the loan.

(C) The principal portion of the payment increases over time.

(D) The interest portion of the payment increases over time.

(E) The total amount paid over the loan tenure equals the original principal.

Question 3. To calculate the EMI for a loan, which inputs are typically required?

(A) Principal loan amount

(B) Annual interest rate

(C) Loan tenure (in years or months)

(D) The borrower's monthly income

(E) The effective annual rate

Question 4. If a loan is for $P$ with an annual interest rate $R$ compounded monthly for $N$ years, and EMIs are paid monthly, select the correct parameters for the EMI formula.

(A) Principal = $P$

(B) Periodic Interest Rate = $R/12$ (as a decimal)

(C) Number of Periods = $N \times 12$

(D) Periodic Interest Rate = $R$ (as a decimal)

(E) Number of Periods = $N$

Question 5. Which of the following statements are true about an Amortization Schedule?

(A) It details how each EMI is split between principal and interest.

(B) It shows the remaining loan balance after each payment.

(C) The sum of the interest components over all periods equals the total interest paid on the loan.

(D) The sum of the principal components over all periods equals the original loan amount.

(E) It shows the future value of the loan.

Question 6. How do changes in interest rates and loan tenure affect the EMI, assuming a fixed principal amount?

(A) A higher interest rate increases the EMI.

(B) A shorter loan tenure increases the EMI.

(C) A lower interest rate decreases the EMI.

(D) A longer loan tenure increases the EMI.

(E) Changes in interest rate have no effect on EMI.

Question 7. If you prepay a part of your loan principal, which of the following effects might occur?

(A) The remaining loan tenure might decrease (if EMI is kept constant).

(B) The EMI might decrease (if tenure is kept constant).

(C) The total interest paid over the life of the loan will decrease.

(D) The principal amount of subsequent EMIs will decrease.

(E) The interest rate on the loan might increase.

Question 8. The process of paying off a loan over time through a series of periodic payments is called:

(A) Compounding

(B) Accumulation

(C) Amortization

(D) Sinking Fund

(E) Depreciation

Question 9. When is the EMI concept typically used?

(A) For long-term loans like home loans or car loans.

(B) For personal loans repaid over a fixed period.

(C) For recurring deposits where you save a fixed amount periodically.

(D) For investments earning simple interest.

(E) For calculating the present value of a single future sum.

Question 10. In the early years of a long-term loan with EMIs, a larger portion of the payment goes towards ________, while in the later years, a larger portion goes towards ________.

(A) Principal, Interest

(B) Interest, Principal

(C) Fees, Taxes

(D) Principal, Fees

(E) Interest, Interest (portion remains constant)

Question 1. Select all correct statements about Absolute Return.

(A) It is the total gain or loss on an investment in monetary terms.

(B) It is calculated as Final Value - Initial Value.

(C) It is expressed as a percentage.

(D) It considers the time period of the investment.

(E) It is the same as the percentage return.

Question 2. Select all correct ways to calculate the Percentage Return on an investment over a period.

(A) $(\text{Final Value} - \text{Initial Value}) / \text{Initial Value}$

(B) $(\text{Final Value} / \text{Initial Value}) - 1$

(C) $\text{Absolute Return} / \text{Initial Value}$

(D) $(\text{Final Value} - \text{Initial Value}) \times 100$

(E) $\text{Initial Value} / \text{Final Value}$

Question 3. A Nominal Rate of Return is:

(A) The stated return before considering the impact of inflation.

(B) The real rate of return adjusted for inflation.

(C) The return after accounting for taxes.

(D) A rate that does not consider the changing purchasing power of money.

(E) Used to calculate Compound Annual Growth Rate (CAGR).

Question 4. What does Compound Annual Growth Rate (CAGR) represent?

(A) The average annual growth rate over a specific period.

(B) The constant rate at which an investment would have grown annually to reach its final value from its initial value, assuming compounding.

(C) A smoothed representation of growth that dampens volatility.

(D) The simple average of yearly returns.

(E) The highest return achieved in any single year during the period.

Question 5. The formula for CAGR is given by $(\text{End Value} / \text{Start Value})^{1/n} - 1$, where $n$ is the number of years. Which of the following are correct statements about this formula?

(A) $n$ is the number of compounding periods.

(B) $n$ is the number of years over the investment period.

(C) It assumes annual compounding over the period.

(D) If $End Value < Start Value$, CAGR will be negative.

(E) If $End Value = Start Value$, CAGR will be 1.

Question 6. Which of the following are appropriate uses for CAGR?

(A) Comparing the growth of two different companies over a 5-year period.

(B) Comparing the performance of two mutual funds with different track records (length).

(C) Evaluating the growth of revenue, profits, or market share over time.

(D) Calculating the required rate of return for an investment.

(E) Measuring the return on a simple interest deposit for one year.

Question 7. If an investment grows from $\textsf{₹}50,000$ to $\textsf{₹}60,000$ in 2 years, which of the following calculations are correct?

(A) Absolute Return = $\textsf{₹}10,000$

(B) Percentage Return = 20%

(C) CAGR = $(60000/50000)^{1/2} - 1$

(D) CAGR = $\sqrt{1.2} - 1 \approx 0.0954$ or 9.54%

(E) Simple Average Annual Return = 10%

Question 8. CAGR provides a more accurate picture of cumulative growth than simple average return when:

(A) The investment period is exactly one year.

(B) Returns fluctuate significantly from year to year.

(C) Comparing growth over multiple periods.

(D) The investment earns simple interest.

(E) The initial and final values are the same.

Question 9. Which of the following are limitations of using CAGR?

(A) It ignores the volatility of returns within the period.

(B) It assumes a smooth, constant growth rate, which is rarely the case in reality.

(C) It is not suitable for comparing investments over different time horizons.

(D) It does not tell you anything about the actual intermediate values.

(E) It requires knowing the monthly returns.

Question 10. If an investment loses value over a period, which of the following are true?

(A) The Absolute Return is negative.

(B) The Percentage Return is negative.

(C) The CAGR is negative.

(D) The Final Value is less than the Initial Value.

(E) Simple interest was applied.

Question 1. Select all correct reasons why businesses depreciate assets.

(A) To allocate the cost of the asset over its useful life.

(B) To account for wear and tear, obsolescence, or usage of the asset.

(C) To match the expense of using the asset with the revenue it helps generate.

(D) It is a tax-deductible expense, reducing taxable income.

(E) To determine the current market value of the asset.

Question 2. The Straight-Line Method of Depreciation requires which of the following information?

(A) The original cost of the asset.

(B) The estimated useful life of the asset.

(C) The estimated salvage value (scrap value) of the asset.

(D) The market value of the asset at the end of each year.

(E) The production output from the asset each year.

Question 3. Select all correct formulas for calculating the annual depreciation expense using the Straight-Line Method.

(A) $\frac{\text{Cost of Asset} - \text{Salvage Value}}{\text{Useful Life (in years)}}$

(B) $\frac{\text{Depreciable Amount}}{\text{Useful Life}}$

(C) $\frac{\text{Cost of Asset}}{\text{Useful Life}}$ (only if Salvage Value is zero)

(D) Cost of Asset $\times$ Depreciation Rate (where Rate is 1/Useful Life)

(E) Beginning Book Value $\times$ Depreciation Rate

Question 4. What is Book Value?

(A) The original cost of an asset.

(B) The market value of an asset.

(C) The value of an asset on the company's balance sheet.

(D) Calculated as Original Cost - Accumulated Depreciation.

(E) Calculated as Original Cost - Salvage Value.

Question 5. A machine costs $\textsf{₹}1,00,000$, has a useful life of 5 years, and a salvage value of $\textsf{₹}10,000$. Which of the following are true when using the Straight-Line Method?

(A) Depreciable amount = $\textsf{₹}90,000$.

(B) Annual Depreciation = $\textsf{₹}18,000$.

(C) Annual Depreciation = $\textsf{₹}20,000$.

(D) Book value at the end of Year 1 = $\textsf{₹}82,000$.

(E) Book value at the end of Year 5 = $\textsf{₹}10,000$.

Question 6. Accumulated Depreciation represents:

(A) The total depreciation expense charged on an asset since its acquisition.

(B) A contra-asset account on the balance sheet.

(C) The loss on sale of an asset.

(D) The sum of annual depreciation expenses up to a point in time.

(E) The salvage value.

Question 7. Which of the following statements are correct about the Straight-Line Depreciation method?

(A) It results in a constant depreciation expense each year.

(B) The book value decreases linearly over the asset's useful life.

(C) It is the simplest depreciation method.

(D) It is the most commonly used method for tax purposes in some jurisdictions.

(E) It recognizes higher depreciation expense in the early years of an asset's life.

Question 8. If an asset is sold for more than its book value, which of the following statements are true?

(A) There is a gain on the sale of the asset.

(B) The gain is calculated as Selling Price - Book Value.

(C) There is a loss on the sale of the asset.

(D) Depreciation was overstated.

(E) The accumulated depreciation is zero.

Question 9. The Salvage Value is the estimated value of an asset:

(A) At the beginning of its useful life.

(B) When it is purchased.

(C) At the end of its useful life.

(D) If it were sold for scrap or residual value.

(E) Which is always zero.

Question 10. Depreciation is relevant in which of the following areas?

(A) Financial Accounting (determining profit and asset values).

(B) Tax Calculation (reducing taxable income).

(C) Investment Analysis (evaluating the cost of using an asset).

(D) Pricing Strategy (factoring in asset usage cost).

(E) Calculating simple interest on a loan.

Question 1. Which of the following are characteristics of Direct Taxes?

(A) The burden of the tax falls directly on the person who pays it to the government.

(B) Examples include Income Tax and Corporate Tax.

(C) They are typically based on income or wealth.

(D) The tax is passed on to the final consumer.

(E) Goods and Service Tax (GST) is a direct tax.

Question 2. Which of the following are characteristics of Indirect Taxes?

(A) The burden of the tax can be shifted to another person (usually the consumer).

(B) Examples include GST, VAT (historically), and Excise Duty (historically).

(C) They are typically levied on goods and services.

(D) The person who collects the tax from the consumer pays it to the government.

(E) Income Tax is an indirect tax.

Question 3. Taxable Income is calculated by adjusting Gross Total Income for which of the following?

(A) Deductions allowed under the Income Tax Act (e.g., under Section 80C, 80D, etc.).

(B) Exemptions provided for certain types of income.

(C) Tax already paid (TDS or Advance Tax).

(D) Surcharges and Cess.

(E) GST paid on purchases.

Question 4. Tax Slabs determine:

(A) The different rates of tax applicable to different ranges of taxable income.

(B) That income tax is a progressive tax (typically, higher income falls into higher slabs).

(C) The amount of tax payable for a specific income level.

(D) The types of deductions available.

(E) The rate of GST.

Question 5. If a person has a taxable income of $\textsf{₹}8,00,000$ and the tax slabs are: $0-2.5$ Lakh ($0\%$), $2.5-5$ Lakh ($5\%$), $5-10$ Lakh ($20\%$), which of the following calculations are correct for the tax liability (ignoring cess/surcharge)?

(A) Tax on the first $\textsf{₹}2,50,000$ is $\textsf{₹}0$.

(B) Tax on income between $\textsf{₹}2,50,001$ and $\textsf{₹}5,00,000$ is $5\%$ of $\textsf{₹}2,50,000$.

(C) Tax on income between $\textsf{₹}5,00,001$ and $\textsf{₹}8,00,000$ is $20\%$ of $\textsf{₹}3,00,000$.

(D) Total tax liability is $\textsf{₹}12,500 + \textsf{₹}60,000 = \textsf{₹}72,500$.

(E) The entire income of $\textsf{₹}8,00,000$ is taxed at $20\%$.

Question 6. Goods and Service Tax (GST) is a tax on the supply of goods and services. Which of the following are true about GST?

(A) It replaced multiple indirect taxes in India.

(B) It is a consumption-based tax.

(C) It operates on the principle of Input Tax Credit (ITC).

(D) It is levied at a single rate across all goods and services.

(E) It is collected by the Central Government only.

Question 7. Input Tax Credit (ITC) in GST allows a registered business to:

(A) Reduce their final tax liability by the tax paid on their purchases of inputs.

(B) Claim a refund of taxes paid on all business expenses.

(C) Pay tax only on the value addition at each stage of the supply chain.

(D) Avoid paying any GST on sales.

(E) Reduce their income tax liability.

Question 8. If a product's base price is $\textsf{₹}2,500$ and the applicable GST rate is $18\%$, which of the following are correct?

(A) GST amount = $18\%$ of $\textsf{₹}2,500$.

(B) GST amount = $\textsf{₹}450$.

(C) Total price including GST = $\textsf{₹}2,500 + \textsf{₹}450$.

(D) Total price including GST = $\textsf{₹}2,950$.

(E) The GST is paid by the seller to the government, but effectively borne by the buyer.

Question 9. Tax liability calculation can involve:

(A) Identifying the relevant tax slabs for income tax.

(B) Calculating tax on different portions of income at varying rates.

(C) Adding surcharges and cess to the basic tax amount.

(D) Applying the correct GST rate to the value of goods or services.

(E) Calculating simple interest on the principal amount.

Question 10. Which of the following are generally considered types of income that might be subject to Income Tax in India?

(A) Salary income

(B) Income from house property (rental income)

(C) Profits and gains from business or profession

(D) Capital gains (profit from selling assets)

(E) GST collected on sales

Question 1. A typical utility bill (like electricity, water, or gas) usually includes which of the following components?

(A) Charges based on the quantity of the utility consumed (usage).

(B) A fixed charge or standing charge that is constant regardless of usage.

(C) Taxes and duties (like GST).

(D) Surcharges or service charges.

(E) Income tax of the consumer.

Question 2. Tariff Rates on a utility bill tell you:

(A) The total amount due.

(B) The price per unit of consumption (e.g., $\textsf{₹}$/kWh, $\textsf{₹}$/litre, $\textsf{₹}$/SCM).

(C) How the charge varies with different levels of consumption (in tiered tariffs).

(D) The date by which the bill is due.

(E) The initial meter reading.

Question 3. In a tiered (slab) electricity tariff structure where rates increase with consumption, if a consumer uses $400$ units and the slabs are $0-100$ units @ $\textsf{₹}4$/unit, $101-300$ units @ $\textsf{₹}6$/unit, Above $300$ units @ $\textsf{₹}8$/unit, which calculations are correct for the energy charge?

(A) Charge for the first $100$ units = $100 \times \textsf{₹}4$.

(B) Charge for the next $200$ units = $200 \times \textsf{₹}6$.

(C) Charge for the remaining $100$ units = $100 \times \textsf{₹}8$.

(D) Total energy charge = $\textsf{₹}400 + \textsf{₹}1,200 + \textsf{₹}800$.

(E) The entire $400$ units are charged at $\textsf{₹}8$/unit.

Question 4. Fixed Charges on a utility bill cover costs such as:

(A) Meter maintenance and reading costs.

(B) Infrastructure costs (e.g., lines, pipes, substations).

(C) Customer service costs.

(D) The variable cost of producing the utility.

(E) The cost of the raw material (coal for electricity, raw water).

Question 5. A Surcharge on a bill might be levied for which of the following reasons?

(A) As a penalty for late payment.

(B) To recover fluctuations in fuel costs (like a Fuel Adjustment Surcharge on electricity bills).

(C) To cover specific regulatory costs.

(D) As a reward for timely payment.

(E) As a mandatory discount.

Question 6. Reading and interpreting a utility bill correctly allows consumers to:

(A) Verify the accuracy of the charges.

(B) Understand their consumption patterns.

(C) Identify ways to reduce future bills by controlling usage.

(D) Calculate the exact amount of GST paid.

(E) Negotiate lower tariff rates.

Question 7. How is the 'Usage' or 'Consumption' for a billing period typically determined from meter readings?

(A) By reading the meter once at the end of the period.

(B) By reading the meter at the beginning and end of the period and finding the difference.

(C) Based on an estimated value if a reading is not taken.

(D) By checking the total cumulative usage shown on the meter.

(E) By dividing the total bill amount by the tariff rate.

Question 8. A Service Charge on a bill might cover the cost of:

(A) Providing the basic utility service itself (like delivering power or water).

(B) Maintaining the connection infrastructure up to the consumer's premises.

(C) Specific administrative tasks like billing or account management.

(D) Meter inspection and maintenance.

(E) Consumption units.

Question 9. Which of the following are important details to check on an electricity bill?

(A) The meter readings (present and previous).

(B) The calculated consumption (present reading - previous reading).

(C) The applicable tariff rates and how they are applied (slab breakdown).

(D) Any fixed charges, surcharges, or additional fees.

(E) The total accumulated interest.

Question 10. If your water bill shows a consumption of $10,000$ litres and the rate is $\textsf{₹}18$ per $1,000$ litres, plus a fixed charge of $\textsf{₹}80$, which of the following are correct calculations for the bill (ignoring other charges)?

(A) Usage charge = $10 \times \textsf{₹}18$.

(B) Usage charge = $\textsf{₹}180$.

(C) Total bill = $\textsf{₹}180 + \textsf{₹}80$.

(D) Total bill = $\textsf{₹}260$.

(E) Usage charge = $10000 \times \textsf{₹}18$.