Question

A $5,000 bond with a coupon rate of 5.3% paid semiannually has eight years to maturity and a yield to maturity of 6.9%. If interest rates fall and the yield to maturity decreases by 0.8%, what will happen to the price of the bond? O A. fall by $235.32 O B. rise by $235.32 O C. fall by $282.39 O D. rise by $329.45

Answer 1

Interest rate 6.9%:

Coupon = (0.053 * 5000) / 2 = 132.5

Number of periods = 8 * 2 = 16

Rate = 6.9% / 2 = 3.45%

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

Price = 132.5 * [1 - 1 / (1 + 0.0345)¹⁶] / 0.0345 + 5000 / (1 + 0.0345)¹⁶

Price = 132.5 * [1 - 0.581182] / 0.0345 + 2,905.909497

Price = 132.5 * 12.139652 + 2,905.909497

Price = $4,514.41341

Interest rate 6.9% - 0.8% = 6.1%

Coupon = (0.053 * 5000) / 2 = 132.5

Number of periods = 8 * 2 = 16

Rate = 6.1% / 2 = 3.05%

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

Price = 132.5 * [1 - 1 / (1 + 0.0305)¹⁶] / 0.0305 + 5000 / (1 + 0.0305)¹⁶

Price = 132.5 * [1 - 0.618347] / 0.0305 + 3,091.733605

Price = 132.5 * 12.513222 + 3,091.733605

Price = $4,749.735555

Change in price = 4,749.735555 - 4,514.41341

Change in price = 235.32

Rise by $235.32