Question

) A bond's market price is $950. It has a $1,000 par value, will mature in 14 years, and has a coupon interest rate of 8 percent annual interest, but makes its interest payments semiannually. What is the bond's yield to maturity? What happens to the bond's yield to maturity if the bond matures in 28 years? What if it matures in 7 years? (Round to two decimal places.) The bond's yield to maturity if it matures in 14 years is % The bond's yield to maturity if it matures in 28 years is % The bond's yield to maturity if it matures in 7 years is %

Answer 1

Answer a.

Par Value = $1,000
Current Price = $950

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4%*$1,000
Semiannual Coupon = $40

Semiannual Period to Maturity = 28 (14 years)

Let semiannual YTM be i%

$950 = $40 * PVIFA(i%, 28) + $1,000 * PVIF(i%, 28)

Using financial calculator:
N = 28
PV = -950
PMT = 40
FV = 1000

I = 4.311%

Semiannual YTM = 4.311%
Annual YTM = 2 * 4.311%
Annual YTM = 8.62%

Answer b.

Par Value = $1,000
Current Price = $950
Semiannual Coupon = $40
Semiannual Period to Maturity = 56 (28 years)

Let semiannual YTM be i%

$950 = $40 * PVIFA(i%, 56) + $1,000 * PVIF(i%, 56)

Using financial calculator:
N = 56
PV = -950
PMT = 40
FV = 1000

I = 4.235%

Semiannual YTM = 4.235%
Annual YTM = 2 * 4.235%
Annual YTM = 8.47%

Answer c.

Par Value = $1,000
Current Price = $950
Semiannual Coupon = $40
Semiannual Period to Maturity = 14 (7 years)

Let semiannual YTM be i%

$950 = $40 * PVIFA(i%, 14) + $1,000 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -950
PMT = 40
FV = 1000

I = 4.489%

Semiannual YTM = 4.489%
Annual YTM = 2 * 4.489%
Annual YTM = 8.98%