What is the present value (rounded to nearest dollar) of a series of bond interest payments of $2,000 each paid semiannually for 4 years when the annual interest rate is 8%?

a.$6,624

b.$11,465

c.$13,465

d.$16,000

The correct answer is C.

Explanation:

Giving the following information:

A series of bond interest payments of $2,000 each paid semiannually for 4 years. The annual interest rate is 8%

First, we need to calculate the real interest rate:

Interest rate = 0.08/2 = 0.04 semiannually

Now, we need to calculate the future value of the cash flow, and then the present value.

Future value:

FV = {A*[ (1+i) ^n-1]}/i

A = semi annual deposit = 2,000

i = 0.04

n = 2*4 = 8

FV = {2,000*[ (1.04^8) - 1]} / 0.04 = $18,428.45

We calculate the present value:

PV = FV / (1+i) ^n

PV = 18,428.45 / (1.04^8) = $13,465.49