Assertion-Reason MCQs for Sub-Topics of Topic 15: Financial Mathematics

Question 1. Assertion (A): The Amount accumulated from an investment is always greater than or equal to the Principal amount.
Reason (R): The Amount is the sum of the Principal and the Interest earned over the period.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): A higher annual interest rate will always result in higher interest earned over a fixed time period, assuming the same principal.
Reason (R): Interest rate is the percentage charged or earned on the principal for a specific period.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Time is a crucial factor in calculating both simple and compound interest.
Reason (R): Interest calculation is typically based on a rate applied over a unit of time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): A periodic interest rate of 1% per month is equivalent to an annual interest rate of 12%.
Reason (R): The annual interest rate is simply the periodic rate multiplied by the number of periods in a year.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Accumulation refers to the increase in the value of an investment or loan over time.
Reason (R): This increase is due to the addition of interest to the principal.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Simple interest is calculated only on the original principal amount.
Reason (R): The formula for simple interest is $I = \frac{P \times R \times T}{100}$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): The amount accumulated under simple interest grows linearly over time.
Reason (R): The interest earned each year remains constant, assuming a fixed principal and rate.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): To calculate simple interest for a period in months, the time ($T$) in the formula should be the number of months.
Reason (R): The rate ($R$) in the simple interest formula is typically given as a percentage per annum, so time must be in years.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): If $\textsf{₹}5,000$ is invested at 10% simple interest per annum, the interest earned in the 3rd year is the same as the interest earned in the 1st year.
Reason (R): In simple interest, interest is calculated on the accumulated amount from the previous period.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): The Amount (A) in simple interest is calculated as $A = P(1 + \frac{RT}{100})$.
Reason (R): The total amount is the sum of the principal and the simple interest ($I = \frac{PRT}{100}$).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Compound interest leads to higher accumulation than simple interest over periods longer than one year, for the same principal and nominal rate.
Reason (R): In compound interest, interest earned in previous periods is added to the principal, and interest is calculated on this new, larger balance in subsequent periods.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): If the annual rate is 12%, compounding monthly will yield a higher amount than compounding annually over the same year.
Reason (R): More frequent compounding within a year results in earning interest on interest more often.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): The amount formula for compound interest compounded $m$ times a year is $A = P(1 + r/m)^{nm}$.
Reason (R): $r/m$ represents the periodic rate and $nm$ represents the total number of compounding periods.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): For a one-year period, simple interest and compound interest are always equal, regardless of the compounding frequency.
Reason (R): If the compounding happens only at the end of the year, there is no opportunity for interest to earn interest within that single year.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): If a sum doubles in 5 years at compound interest, it will become four times in 10 years at the same rate.
Reason (R): In compound interest, the multiplying factor $(1+r)^n$ applies for each period. If it doubles in 5 years, the factor for 5 years is 2. In the next 5 years, it will double again, making the total factor $2 \times 2 = 4$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): The nominal interest rate is the stated or quoted rate, while the effective interest rate reflects the actual annual rate after accounting for compounding.
Reason (R): When interest is compounded more than once a year, the effective rate is higher than the nominal rate (for a positive rate).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Comparing loans or investments with different compounding frequencies requires calculating their effective annual rates.
Reason (R): The effective rate provides a standardised annual rate that accounts for the impact of compounding, allowing for a like-to-like comparison.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): If the nominal rate is 6% per annum compounded monthly, the effective annual rate is exactly 6%.
Reason (R): The effective rate equals the nominal rate only when interest is compounded annually.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): A bank offering 8% per annum simple interest is equivalent to a bank offering 8% per annum compounded annually for a one-year deposit.
Reason (R): For a period of exactly one year, simple interest and compound interest (compounded annually) yield the same amount.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Increasing the compounding frequency (e.g., from quarterly to monthly) while keeping the nominal rate constant increases the effective annual rate.
Reason (R): More frequent compounding allows interest to be earned on previously accumulated interest more often within the year.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): A sum of $\textsf{₹}1,000$ received today is worth more than $\textsf{₹}1,000$ received one year from now.
Reason (R): Money received today can be invested to earn interest, making it grow to a larger amount in the future.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Calculating the Present Value of a future cash flow involves compounding.
Reason (R): Compounding is the process of finding the future value of a present sum.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): According to the Net Present Value (NPV) rule, a project with a positive NPV should be accepted.
Reason (R): A positive NPV indicates that the project is expected to generate returns greater than the required rate of return, thereby adding value to the firm.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The higher the discount rate, the lower the present value of a future cash flow.
Reason (R): A higher discount rate implies a higher opportunity cost or risk, making future money less valuable today.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Net Present Value (NPV) is calculated by subtracting the initial investment from the future value of all cash flows.
Reason (R): NPV is the sum of the present values of all cash inflows minus the present value of all cash outflows.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): An annuity is a series of equal payments made at regular intervals.
Reason (R): Loan EMIs are a common example of an ordinary annuity.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): The future value of an annuity due is always greater than the future value of an ordinary annuity, assuming the same payment, rate, and number of periods.
Reason (R): In an annuity due, each payment is made one period earlier, allowing it to earn interest for one extra period compared to an ordinary annuity.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Calculating the present value of a regular annuity involves discounting each future payment back to time zero.
Reason (R): The present value of an annuity is the sum of the present values of its individual payments.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): If the interest rate is 0%, the future value of an ordinary annuity of $\textsf{₹}100$ per year for 5 years is $\textsf{₹}500$.
Reason (R): With a 0% interest rate, no interest is earned, so the future value is simply the sum of the payments.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Rent payments made at the beginning of each month are an example of an ordinary annuity from the perspective of the tenant.
Reason (R): In an ordinary annuity, payments are made at the end of each period.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): A perpetuity is a series of equal payments that continues indefinitely.
Reason (R): The present value of a perpetuity can be calculated as $Pmt/i$, where $Pmt$ is the periodic payment and $i$ is the periodic interest rate.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): A sinking fund is used to accumulate a specific sum of money by making regular periodic deposits.
Reason (R): Sinking funds are often established to meet future financial obligations like debt repayment or asset replacement.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): If the interest rate increases, the present value of a perpetuity will decrease.
Reason (R): A higher interest rate means future payments are discounted back at a faster rate, making their value lower in today's terms.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Calculating the required periodic contribution to a sinking fund involves solving for the payment amount in the future value of ordinary annuity formula.
Reason (R): The target amount of the sinking fund is the future value that needs to be accumulated by the series of periodic payments.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): A perpetuity has an infinite future value.
Reason (R): Since the payments continue forever, the accumulated amount will also grow infinitely over an infinite time horizon.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): An Equated Monthly Installment (EMI) consists of both a principal repayment component and an interest payment component.
Reason (R): The interest component of the EMI is calculated on the outstanding loan balance at the beginning of the month.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): In the initial EMIs of a loan, the principal component is larger than the interest component.
Reason (R): The outstanding loan balance is highest at the beginning of the loan tenure, resulting in a larger interest calculation for the early EMIs.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): A longer loan tenure results in a lower EMI.
Reason (R): Stretching the loan repayment over a longer period reduces the amount of principal and interest that needs to be repaid each month.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): EMI calculation is based on the present value of an annuity concept.
Reason (R): The loan amount is equivalent to the present value of the stream of future equal EMI payments, discounted at the loan interest rate.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): An amortization schedule shows the break-up of each EMI payment between principal and interest and the remaining loan balance.
Reason (R): Amortization means liquidating or paying off a loan over time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Percentage return is a better metric than absolute return for comparing the performance of investments of different initial sizes.
Reason (R): Percentage return expresses the gain or loss relative to the initial investment amount, providing a standardised measure.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Compound Annual Growth Rate (CAGR) provides a smoothed annual growth rate over a specific period.
Reason (R): CAGR assumes that the investment grew at a constant rate each year, compounding annually over the period.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): If an investment doubles in value over 7 years, its CAGR is approximately 10.4%.
Reason (R): CAGR calculation uses the formula $(End Value / Start Value)^{1/n} - 1$, where $n$ is the number of years.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): CAGR is a suitable metric for comparing investments with different investment durations.
Reason (R): CAGR provides an annualised growth rate, making it easier to compare the performance of investments held for different lengths of time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): A negative CAGR indicates that the investment has lost value over the period.
Reason (R): A negative CAGR means the End Value was lower than the Start Value, resulting in an overall decline.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Depreciation is a process of valuing an asset at its market price each year.
Reason (R): Depreciation is the systematic allocation of the cost of an asset over its useful life to account for its decrease in value due to usage or obsolescence.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Using the Straight-Line Method, the annual depreciation expense is constant over the asset's useful life.
Reason (R): The Straight-Line method divides the depreciable amount (Cost - Salvage Value) equally by the useful life.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): The book value of an asset decreases each year as depreciation is charged.
Reason (R): Book value is calculated as the original cost of the asset minus the accumulated depreciation.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Salvage value is the estimated value of an asset at the beginning of its useful life.
Reason (R): Salvage value is the estimated residual value an asset is expected to have at the end of its useful life.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Depreciation is a non-cash expense but impacts the company's profitability.
Reason (R): Depreciation expense is deducted from revenue in the income statement, reducing net income and taxable income, even though no cash outflow occurs for the depreciation itself.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Income tax is a direct tax.
Reason (R): The burden of income tax falls directly on the income earner who pays it to the government.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Goods and Service Tax (GST) is a direct tax.
Reason (R): GST is levied on the supply of goods and services, and its burden is typically passed on to the final consumer.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Taxable income is always equal to gross total income.
Reason (R): Taxable income is calculated after allowing for various deductions and exemptions from gross total income.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Input Tax Credit (ITC) helps avoid the cascading effect of taxes in GST.
Reason (R): Businesses can use the GST paid on their inputs as a credit against the GST they collect on their outputs.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Tax slabs result in a progressive income tax system in India.
Reason (R): Under tax slabs, a higher rate of tax is applied to higher income brackets.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Utility bills like electricity and water often include a fixed charge regardless of consumption.
Reason (R): Fixed charges cover the costs related to maintaining the infrastructure and services needed to provide the utility, which are not directly proportional to usage.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): In a tiered electricity tariff system, the rate per unit consumed might increase as consumption goes up.
Reason (R): Tiered tariffs are designed to discourage high consumption and promote conservation by making additional units more expensive.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): The usage shown on a utility bill is calculated by adding the present meter reading and the previous meter reading.
Reason (R): Consumption is the difference between the meter reading at the end of the billing period and the reading at the beginning of the period.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Understanding the components of your utility bill can help in managing household expenses.
Reason (R): By identifying consumption patterns and different charges, consumers can make informed decisions to potentially reduce usage or costs.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): A Surcharge on a bill is always a discount for paying on time.
Reason (R): A surcharge is an additional charge, often applied as a penalty for late payment or to cover unexpected costs.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.