Question

Which of the following bank accounts has the highest effective annual return?

a. An account which pays 10% nominal interest with monthly compounding

b. An account which pays 10% nominal interest with daily compounding

c. An account which pays 10% nominal interest with annual compounding

d. An account which pays 9% nominal interest with daily compounding

e. An account which pays 10% nominal interest with quarterly compounding

f. All of the above investments have the same effective annual return

Answer 1

Effective Annual Rate of Return 'R' is calculated by (1 + i/m)^m - 1

where, i - nominal interest rate and m - number of compounding periods/ frequency of compounding in a year

Now a basic fact of compounding is that the more the number of compounding periods the higher will be the effective annual return, because an investment is earning interest by compounding more number of times in the year. Hence, monthly compounding will give higher effective return than quarterly compounding , which will give higher return than semi-annual compounding, and so on.

So, for the nominal interest of 10%, we can safely conclude that daily compounding has the highest effective return which is equal to (1+ 0.1/365)³⁶⁵ - 1 = 10.516% (Use MS Excel for the calculation)

You can verify that this is the highest effective return for the nominal rate of 10% by calculating the same for the other compounding periods as given in options a,c and e.

For option d - 9% nominal interest with daily compounding, R = (1 + 0.09/365)³⁶⁵ - 1 = 9.416%

Hence correct answer is Option B.