Question

1. What is the YTM on a 4-year bond that pays $50 semiannually and has a current price of $1,087.52? Assume the face value is $1,000 and that there is exactly six months before the first interest payment.

2. A 7-year, 8% coupon bond pays interest semi-annually. The bond has a face value of $1,000. What is the price of this bond if the yield to maturity is 4.0%?

3. Find the price of a 15-year zero-coupon bond when the market required rate of return is 9% for a semiannual bond of similar risk.

Answer 1

Answer of Part 1:

Face Value = $1,000

Current Price = $1,087.52
Semiannual Coupon = $50

Time to Maturity = 4 years
Semiannual Period to Maturity = 8

Let semiannual YTM be i%

$1,087.52 = $50 * PVIFA(i%, 8) + $1,000 * PVIF(i%, 8)

Using financial calculator:
N = 8
PV = -1,087.52
PMT = 50
FV = 1,000

I = 3.715%

Semiannual YTM = 3.715%
Annual YTM = 2 * 3.715%
Annual YTM = 7.43%