Question

Consider a 10 year bond with face value $1,000, pays 6% coupon annually and has a yield-to-maturity of 7%. How much would the approximate percentage change in the price of bond if interest rate in the economy decreases by 0.80% per year?

increase by 5.55%

increase by 5.55%

increase by 5.98%

decrease by 5.98%

Answer 1

Coupon = 6% of 1000 = 60

Current price = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Current price = 60 * [1 - 1 / (1 + 0.07)^10] / 0.07 + 1000 / (1 + 0.07)^10

Current price = 60 * [1 - 0.508349] / 0.07 + 508.349292

Current price = 60 * 7.023582 + 508.349292

Current price = $929.7642

Price after decrease in interest rate.

New interest rate = 7% - 0.8% = 6.2%

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

Price = 60 * [1 - 1 / (1 + 0.062)^10] / 0.062 + 1000 / (1 + 0.062)^10

Price = 60 * [1 - 0.547968] / 0.062 + 547.96754

Price = 60 * 7.290846 + 547.96754

Price = $985.4183

Increase = [(Ending value - beginning value) / beginning value] * 100

Increase = [(985.4183 - 929.7642) / 929.7642] * 100

Increase = 5.98%