Question

Calculate the Nominal Interest Rate, the Interest Rate per Compounding Period and the Effective Annual Interest Rate for the following problems:

1. A Bank is offering a saving account at 3% compounded monthly.

2. A Credit Card company says their card charges an APY of 8.5619% compounded quarterly.

3. Nomani wants to earn 0.25% per week.

Answer 1

1. A Bank is offering a saving account at 3% compounded monthly.

Nominal interest rate=i=3%

Number of compounding per year=c=12

Interest rate per compounding period=i/c=3%/12=0.25%

Effective rate of interest=(1+i/c)^c-1=(1+0.25%)^12-1=3.0416%

2. A Credit Card company says their card charges an APY of 8.5619% compounded quarterly.

In this case

Effective rate of interest=ie=8.5619%

Number of compounding per year=c=4

Interest rate per compounding period=i/c=(1+ie)^(1/c)-1=(1+8.5619%)^(1/4)-1=2.0750%

Nominal interest rate=i=(i/c)*c=2.0750%*4=8.30%

3. Nomani wants to earn 0.25% per week.

Interest rate per compounding period=i/c=0.25%

Number of compounding per year=c=52

Nominal interest rate=(i/c)*c=0.25%*52=13.00%

Effective rate of interest=(1+i/c)^c-1=(1+0.25%)^52-1=13.8644%