Question

- 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.
- 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?
- 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?
- 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.

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Forward rate
%
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Maturity
Price
Effective Annual
In years
(per
$1000 in face
value)
YTM
1
985.000
______________
2
952.000
______________
3
917.500
______________
4
871.442
.0350000
5
821.927
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*
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