Your bank account pays a 5% nominal rate of interest.The interest is compounded quarterly.Which of the following statements is CORRECT?
A) The periodic rate of interest is 5% and the effective rate of interest is also 5%.
B) The periodic rate of interest is 1.25% and the effective rate of interest is 2.5%.
C) The periodic rate of interest is 5% and the effective rate of interest is greater than 5%.
D) The periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%.
E) The periodic rate of interest is 2.5% and the effective rate of interest is 5%.

Question

Quizplus · Accepted Answer

The periodic rate of interest is the nominal rate divided by the number of compounding periods per year. In this case, the nominal rate is 5% and it is compounded quarterly, so the periodic rate is 5%/4 = 1.25%.
The effective rate of interest reflects the total amount of interest earned at the end of a year, taking into account compounding. So, we need to use the formula:
Effective rate = (1 + (nominal rate / m))^m - 1
where m is the number of compounding periods per year. Plugging in the values, we get:
Effective rate = (1 + (5%/4))^4 - 1 = 5.12%
Therefore, the correct statement is that the periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%. Option D is the only choice that matches this statement.

Your Bank Account Pays a 5% Nominal Rate of Interest