Question

Yield to maturity. What is the yield of each of the following bonds if interest​ (coupon) is paid semiannual​ly? (Round to two decimal​ places.)

Par Value	Coupon Rate		Years to Maturity	Yield to Maturity	Price
​$1,000.00	12​%		15	​?______	​$1,000.00
​$5,000.00	11​%		10	​?______	​$6,010.00
​$5,000.00	8​%		25	​?______	​$7,120.00
​$1,000.00	7​%		30	​?______	​$700.00

Answer 1

Answer to Part 1:

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

Annual Coupon Rate = 12%
Semiannual Coupon Rate = 6%
Semiannual Coupon = 6%*$1,000 = $60

Time to Maturity = 15 years
Semiannual Period to Maturity = 30

Let semiannual YTM be i%

$1,000 = $60 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)

Using financial calculator:
N = 30
PV = -1000
PMT = 60
FV = 1000

I = 6.00%

Semiannual YTM = 6.00%
Annual YTM = 2 * 6.00%
Annual YTM = 12.00%

Answer to Part 2:

Par Value = $5,000
Current Price = $6,010

Annual Coupon Rate = 11%
Semiannual Coupon Rate = 5.50%
Semiannual Coupon = 5.50% * $5,000 = $275

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$6,010 = $275 * PVIFA(i%, 20) + $5,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -5000
PMT = 275
FV = 6010

I = 6.05%

Semiannual YTM = 6.05%
Annual YTM = 2 * 6.05%
Annual YTM = 12.10%

Answer to Part 3:

Par Value = $5,000
Current Price = $7,120

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $5,000 = $200

Time to Maturity = 25 years
Semiannual Period to Maturity = 50

Let semiannual YTM be i%

$7,120 = $200 * PVIFA(i%, 50) + $5,000 * PVIF(i%, 50)

Using financial calculator:
N = 50
PV = -5000
PMT = 200
FV = 7120

I = 4.26%

Semiannual YTM = 4.26%
Annual YTM = 2 * 4.26%
Annual YTM = 8.52%

Answer to Part 4:

Par Value = $1,000
Current Price = $700

Annual Coupon Rate = 7%
Semiannual Coupon Rate = 3.5%
Semiannual Coupon = 3.5% * $1,000 = $35

Time to Maturity = 30 years
Semiannual Period to Maturity = 60

Let semiannual YTM be i%

$700 = $35 * PVIFA(i%, 60) + $1,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -1000
PMT = 35
FV = 700

I = 3.34%

Semiannual YTM = 3.34%
Annual YTM = 2 * 3.34%
Annual YTM = 6.68%