Question

Assume that you deposit $10,000 today into an account paying 6% annual interest and leave it on deposit for exactly 8 years.

a.   How much will be in the account at the end of 8 years in interest is compounded:

      1. annually?

      2. semiannually?

      3. monthly?

      4. continuously?

b. Calculate the effective annual rate (EAR) for a (1) through a (4) above.

c. Based on your findings in parts a and b, what is the general relationship between the frequency of compounding and EAR?

Answer 1

a.

Future value = Present value x (1+Rate/Frequency)^(Frequency x Years)

1.

Future value = 10000 x (1+6%/1)^(1 x 8) = 15,938.48

2.

Future value = 10000 x (1+6%/2)^(2 x 8) = 16,047.06

3.

Future value = 10000 x (1+6%/12)^(12 x 8) = 16,141.43

4.

Future value = Present value x Exp(Rate x Years)

Future value = 10000 x Exp(6% x 8) = 16,160.74

b.

EAR = (1+Rate/n)^n -1

1.

EAR = (1+6%/1)^1 -1 = 6.00%

2.

EAR = (1+6%/2)^2 -1 = 6.09%

3.

EAR = (1+6%/12)^12 -1 = 6.17%

4.

EAR = Exp(6%)-1 = 6.18%

c.

As compounding frequency increases the future value increases. Compounding frequency and future value have direct relationship