Test on Compound interest calculations

Question 1: Compound interest represents the interest earned on both the initial principal and the accumulated interest from previous periods.

A. Yes

B. No

Explanation: Compound interest is defined as the interest earned on both the initial principal and the accumulated interest from previous periods, often referred to as 'interest on interest'.

Question 2: In the basic compound interest formula, 'i' represents the total annual interest rate, without any division for compounding periods.

A. Yes

B. No

Explanation: The study materials state that 'i' represents the 'Interest Rate per Compounding Period', which is the annual interest rate divided by the number of compounding periods per year. It is not simply the total annual interest rate.

Question 3: In the compound interest formula A = P · (1 + i)ⁿ, what does 'n' specifically represent?

A. The total number of years the investment is held.

B. The annual interest rate expressed as a decimal.

C. The total number of times interest is compounded over the investment horizon.

D. The number of compounding periods per year.

Explanation: According to the study materials, 'n' represents 'the total number of times interest is compounded over the investment horizon'. This means it accounts for both the duration and the frequency of compounding.

Question 4: When calculating the final amount using the compound interest formula A = P · (1 + i)ⁿ, what critical step must be taken to ensure consistency between the interest rate and the number of periods if the interest is compounded more than once a year?

A. The annual interest rate must be used directly, and the number of periods (n) should solely be the total number of years.

B. The interest rate (i) must be divided by the number of compounding periods per year, and the number of periods (n) must be the number of years multiplied by the number of compounding periods per year.

C. The principal amount (P) should be adjusted based on the compounding frequency, while the annual interest rate and total years remain unchanged.

D. The interest rate (i) should be multiplied by the number of compounding periods per year, and the number of periods (n) should be the total number of years divided by the number of compounding periods per year.

Explanation: The study materials state: 'It is critical to ensure that the interest rate (i) and the number of periods (n) are consistent with the compounding frequency. For instance, if an annual interest rate is 6% and interest is compounded monthly, then i would be 0.06 / 12 = 0.005, and n would be the number of years multiplied by 12.' This directly supports option B, which explains how to adjust 'i' and 'n' for consistency.

Question 5: For the same annual interest rate, less frequent compounding results in significantly higher returns compared to more frequent compounding.

A. Yes

B. No

Explanation: More frequent compounding leads to slightly higher returns for the same annual rate, as interest starts earning interest sooner. Therefore, less frequent compounding would lead to slightly lower, not significantly higher, returns.