Question

13. Consider a bank account with a stated yearly compound interest rate of 4.25%. Assume that

    there is no taxation. Which of the following statements is correct?

    a) If interest is paid monthly, the APR of the account is between 4.1% and 4.3%. b) If interest is paid quarterly, the APR of the account is between 4.1% and 4.3%.

    c) If interest is paid only every two years, the APR of the account is between 4.1% and 4.3%. d) If interest is paid only every ten years, the APR of the account is between 4.1% and 4.3%.

    e) None of the above 4 statements (a) - (d) is correct.

Answer 1

• Given annual interest rate = 4.25 %

a. Hence on a monthly basis = 4.25/12 = 0.3541 %

Therefore on an annual basis APR = (1.003541)¹² = 1.043329 = 4.33 % Hence false.

b. Hence on a quaterly basis = 4.25/4 = 1.0625 %

Therefore on an annual basis APR = (1.010625)⁴ = 1.0431 = 4.31 % Hence false

c. Hence on a two year basis = 4.25*2 = 8.5%

Therefore on an annual basis APR = (1.0085)^.5 = 1.0416 = 4.16 % Hence true

d. Hence on a ten year basis = 4.25*10 = 42.5%

Therefore on an annual basis APR = (1.425)^.1 = 1.036 = 3.6 % Hence false