Which of the following would have the highest effective annual rate for the same nominal annual rate? A. annual interest compounding B. semi-annual interest compounding C. quarterly interest compounding D. monthly interest compounding

D. monthly interest compounding

Explanation:

Monthly compounded rate is highly effective rate from all other available rates. because monthly interest income received are also compounded with principal. Number of compounding in monthly rate is more than all others.

Suppose:

Amount of Investment = $100

Annual Interest = 12%

Annual amount of Interest Income = $100 x 12% = $12

Semi-annual amount of Interest Income = $100 x (1 + (12%/2)) ^2 = $112.36

Quarterly amount of Interest Income = $100 x (1 + (12%/4)) ^4 = $112.55

Monthly amount of Interest Income = $100 x (1 + (12%/12)) ^12 = $112.68

Hence proved that Monthly interest compounding is most effective rate.