Question

Suppose you purchased a corporate bond with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments. This means that you receive a $50 interest payment at the end of each six-month period for 10 years (20 times). Then, when the bond matures, you will receive the principal amount (the face value) in a lump sum. Three years after the bonds were purchased, the going rate of interest on new bonds fell to 6% (or 6% compounded semiannually). What is the current market value (P) of the bond (three years after its purchase)?

Answer 1

The Current market value(P) of the bond 3 years after its purchase=$957.94

Step-by-step explanation:

Current market value(P) after 3 years=Semiannual coupon×(1-(1/1+r)^i)/r+face value/(1+r)^i

where;

i=maturity period=3×2=6 periods

r=10%/2=5%

face value=$1,000

Semi-annual coupon=(5/100)×1,000=$50

replacing;

Current market value(P) after 3 years=50×(1-(1/1+0.05)^6)/0.06+(1000/(1+0.05)^6)

Current market value(P) after 3 years=50×(1-0.746)/0.06+(1000/1.34)

Current market value(P) after 3 years=211.67+746.27

Current market value(P) after 3 years=$957.94