Question

What is the effective monthly interest rate for a loan with a 8% nominal annual interest rate if the loan is compounded (a) monthly, (b) daily, or (c) continuously?

A friend offers you a loan at an effective daily interest rate of 0.2%. (a) What is the nominal (also known as the APR or Annual Percentage Rate) rate for this loan? (b) What is the effective annual interest rate for his loan?

Show all work please

Answer 1

1)

Given

Nominal annual Interest rate R=8%

a) Monthly compounding

Monthly interest rate r=8%/12=0.667%

So Effective interest rate =(1+r)^12-1=(1+0.667%)^12-1=8.30%

b)

Daily compounding

Daily interest rate r=8%/365=0.0219%

So Effective interest rate =(1+r)^365-1=(1+0.0.219%)^365-1=8.32%

c)

Continuous compounding

So Effective interest rate =e^R -1=e^8%-1=8.33%

2) Effective daily rate r=0.2%

A) APR=365*r=365*0.2%=73%

B) Effective interest rate= (1+r)^365-1=(1+0.2%)^365-1=107.36%