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%

The answer is option d. The periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%

Explanation:

Step 1: Determine stated interest rate

The stated interest rate=nominal interest rate=5%

Step 2: Determine periodic interest rate

The periodic interest rate can be expressed as;

periodic interest rate=stated interest rate/number of compounding periods

where;

stated interest rate=5%=5/100=0.05

number of compounding periods=4

replacing;

periodic interest rate=0.05/4=0.0125×100=1.25%

The periodic interest rate=1.25%

Step 3: Determine effective interest rate

The formula for calculating the effective interest rate can be expressed as;

Effective interest rate={(1+i/n)^n}-1

where;

i=stated interest rate=0.05

n=number of compounding periods in a year=4

replacing;

Effective interest rate={(1+0.05/4)^4}-1

Effective interest rate=0.051×100=5.1%