Question

You are considering a 10-year, $1,000 par value bond. Its coupon rate is 9%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 8.16%, then how much should you be willing to pay for the bond?

Present value=

payment=

future value=

annual rate=

periods=

compounding=

Answer 1

Par value= future value= $1,000

Time= 10 years*2= 20 semi-annual periods

Coupon rate= 9%/2= 4.50%

Coupon payment= 0.045*1,000= $45

Effective annual rate= 8.16%

Effective annual rate is calculated using the below formula:

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

Where r is the interest rate and n is the number of compounding periods in one year.

0.0816= (1+r/2)^2 -1

        = 1.0824-1

        = 0.0824*100= 8.24%

(0.0816- 1)^1/2= 1 + r/2

r= 0.08*100

      = 8%

The price of the bond is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 45

N= 20

PMT= 45

I/Y= 4

Press the CPT key and PV to compute the present value.

The value obtained is 1,067.95.

Therefore, I will be willing to pay $1,067.95 for the bond.

In case of any query, kindly comment on the solution.