Question

Consider a 3-year risk-free bond, which pays annual coupons. The coupon rate is 3.5% and the face value is 500. The bond is issued at time t=0, pays coupons at time t=1,2,3 and face value at time t=3. You purchase the bond at time t=0. While holding the bond, you do not reinvest the coupon payments.

What is the future value, at time t=2, of the coupon payments you received if you held the bond from t=0 to maturity?

What is the duration of the bond at t = 0? Assume a yield to maturity of 3.25%. Using this information calculate the approximate percentage price change if yield falls to 3.05%?

Answer 1

The coupons are not reinvested so the future value will be just the sum of coupons received

future value at t=2 of the coupon payments = face value * coupon rate *2 = 500*3.5%*2 = 35

Duration is the weighted average time

Duration = sum of present value of time weighted cashflows / sum of present value of cash flows

= 1460.24 / 503.52 = 2.90

Year (t)	Cash flows	Discounting factor = 1 / ( 1+r)^n	Present value	Present value of time weighted cashflow
1	17.5	0.968523002	16.94915254	16.94915254
2	17.5	0.938036806	16.41564411	32.83128822
3	517.5	0.908510224	470.1540409	1410.462123
Total	503.5188375	1460.242563

Duration of 2.9 means if the interest rate falls by 1% price will increase by 2.9%

Percentage change in price = 2.9 *3.05 = 8.845%