Question

A $5,000 bond had a coupon rate of 5.50% with interest paid semi-annually. Ali purchased this bond when there were 6 years left to maturity and when the market interest rate was 5.75% compounded semi-annually. He held the bond for 3 years, then sold it when the market interest rate was 5.25% compounded semi-annually.

a. What was the purchase price of the bond?

Round to the nearest cent.

b. What was the selling price of the bond?

Round to the nearest cent.

c. What was Ali's gain or loss on this investment?

(click to select)GainLoss

amount was $

.

Answer 1

a. Par value =5000
Semi annual Coupon =5.5%*5000/2 =137.5
Number of Periods =6*2 =12
Semi annual Interest rate =5.75%/2 =2.875%
Purchase Price of the bond =PV of  Coupons+PV of Par value =137.50*((1-(1+2.875%)^-12)/2.875%)+5000/(1+2.875%)^12
=4937.32

b. Par value =5000
Semi annual Coupon =5.5%*5000/2 =137.5
Number of Periods left =3*2 =6
New Semi annual Interest rate =5.25%/2 =2.625%
Sales Price of the bond =PV of  Coupons+PV of Par value =137.50*((1-(1+2.625%)^-6)/2.625%)+5000/(1+2.625%)^12
=5034.28

c. Gain =Sales Price of the bond-Purchase Price of the bond +6*Coupons =5034.28-4937.32+6*137.5 =921.96