Question

a. A bank advertises that customers can borrow money for only 6% interest. However, the loan would be compounded monthly, so what is the effective interest rate on the loan? Loan Effective Annual Rate =

b. A recently purchased bond pays 8% nominal interest, compounded quarterly. What is the effective annual interest rate paid by the bond?

Effective Interest Rate =

c. Your friend's bank offers a savings account that pays an effective annual interest rate of 6.71%. If your bank is offering you a new account that is compounded semiannually, how large must its nominal rate be to have the same effective rate as your friend's account?

Nominal Interest Rate =     

Answer 1

Question Summary : Question on Effective interest rates

Solution: The effective annual interest rate is the rate of interest that an investor can earn (or pay) in a year after taking into consideration compounding over time preriod

Formula :

effective annual interest rate = (1 + i /n ) ^n - 1

where:i=Nominal interest rate n=Number of periods​

a) Answer = Effective Interest rate is 6.17%

i=Nominal interest rate = 6% n=Number of periods​ =12 as it is monthly

EIR =  (1 + (0.06 / 12)) ^ 12 - 1

= ( 1 +0.005) ^12 - 1

= 1.0617 - 1

= 0.0617 or 6.17%

b) Answer = Effective Interest rate is 8.24 %

i=Nominal interest rate = 8% n=Number of periods​ =4 as it is quarterly

EIR =  (1 + (0.08 / 4)) ^ 4 - 1

= ( 1 +0.02) ^4 - 1

= 1.0824 - 1

= 0.0824 or 8.24 %

c) Answer = Nominal Interest rate is 6.6 %

effective annual interest rate of 6.71% n=Number of periods​ =2 as it is semi annually

0.0671 =  (1 + (i / 2)) ^ 2 - 1

1.0671= (1 + (i / 2)) ^ 2

Square root of 1.0671= (1 + (i / 2))

1.0330 = ( 2 + i )/ 2

1.0330*2 - 2 = i

i =0.066 = 6.6%