Question

Suppose a​ ten-year,

$ 1 comma 000$1,000

bond with an

8.2 %8.2%

coupon rate and semiannual coupons is trading for

$ 1 comma 034.97$1,034.97.

a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)?

b. If the​ bond's yield to maturity changes to

9.2 %9.2%

​APR, what will be the​ bond's price?

Answer 1

a)

Coupon = (0.082 * 1000) / 2 = 41

Number of periods = 10 * 2 = 20

Yield to maturity = 7.69%

Keys to use in a financial calculator: 2nd I/Y 2, FV 1000, N 20, PMT 41, PV - 1,034.97, CPT I/Y

b)

Rate = 9.2% / 2 = 4.6%

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 41 * [1 - 1 / (1 + 0.046)²⁰] / 0.046 + 1000 / (1 + 0.046)²⁰

Price = 41 * 12.89595 + 406.78629

Price = $935.52

You can also fins this using a financial calculator:

2nd I/Y 2

FV 1000

PMT 41

N 20

I/Y 9.2

CPT PV