Question

Suppose a​ ten-year,

$1,000

bond with an

8.8%

coupon rate and semiannual coupons is trading for

$1,035.09.

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

9.7%

​APR, what will be the​ bond's price?

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

Answer 1

Bonds are financial instruments that provide fixed returns to its holders. Bonds actually have a nature of debt with a fixed interest rate and a maturity, also known as Plain Vanilla Bond. Some bonds have a callability feature which enables the issuer to call and buy back the bonds from the bondholders.

Yield is the return generated on the bond investment. It considers the future cash flows from the bond and variations in the price of the bond.

It can be calculated as:

Part (a)

Where C denotes the Coupon amount, 8.8% of $ 1,000 = $ 88/2 = $ 44 (Semi-annual coupons)

r denotes Yield to Maturity, (r here denotes the semi-annual yield)

n denotes the Time to Maturity or 10*2 = 20

Substituting the above values, calculate r:

Thus, YTM as an APR is 0.041386 * 2 = 0.082772 or 8.277%

Part (b)

If the YTM changes to 9.7% then calculate the Price by substituting:

C as 8.8% of $ 1,000 = $ 88/2 = $ 44 (Semi-annual coupons)

r as 0.097/2 = 0.0485

n as10*2 = 20

Thus, the Price can be calculated as:

Thus, the Price of the bond when YTM is 9.7% is $ 943.20