Question

1. Currently, the yield‐to‐maturity on zero‐coupon 10‐year US Treasury bonds is 0.66% (0.0066 < 1%). You buy these bonds at $936 per bond and plan to keep them as a “safe” long‐term investment (say, 4 – 5 years). The face value is $1,000 at maturity.
   1. Suppose that, starting next year, interest rates start increasing at a speed of 1% per year (1.6% in 2021, 2.6% in 2022 and so on) and the yield on these bonds follow a similar upward trend. What will the prices of the 10‐year bonds in years 2021 through 2030? What will be your rate of return if you sell your bonds in 2023?
   2. Suppose interest rates do not change much but the average rate of inflation over the next 10 years turns out to be 2.5% per year. What will be your real rate of return if you keep the bonds until maturity?
   3. Do you still want to invest in these bonds? Why or why not?

Answer 1

a. price of 10 -year bond in years 2021 through 2030 = 936 * 1.6 *2.6...........*10.6 = $ 158.7456 * 108

Rate of return if you sell biond in 2023 = 936* 1.6*2.6*3.6 - 936 / 936 = 13.976%

b. Inflation adjusted real rate return = (1+ stock return)/(1+ inflation) - 1 = ( 1+ .66/100)/ (1+2.5/100) -1 = - 0.01795 *100 = - 1.795 %

= 936 (1 - 1.795/100)^10 = 780.93

real rate of return = 780.93 -936/936 = - 16.567%

c. bond value at maturity = 936( 1+ 0.66/100)^10 = 999.64 ~ 1000

bond return = 1000 -936 /936 = 6.8376%

so it is good enough,if inflation is not there , in this way i like to invest in these bond.