Answer : price of a one-year $1000 par Treasury bond with 2% coupons = 977.993
Working notes for the above answer
We have provided with the information that,
Six-month Treasury spot rate is 1.6% APR,
The one-year rate is 2% APR, both compounded semiannually.
What is the price of a one-year $1000 par Treasury bond with 2% coupons?
The calculation for price of a one-year $1000 par Treasury bond with 2% coupons is as follow
| Present Value of Interest Payments = c × F × | 1 − (1 + r)-t |
| r |
The present value of the face value (i.e. the maturity value) is calculated as follows:
| Present Value of Face Value of a Bond = | F |
| (1+r)t |
Therefore, the price of a bond is given by the following formula:
| Present Value of bond = c × F × | 1 − (1 + r)-t | + | F |
| r | (1 + r)t |
we put the figures in the above formulla
=1% x 1000 x 1 – (1 +1%)2 / 1% + 1000 /(1 +1%)2
= 1% * 1000 * -0.002 + 998.003
| = 977.993 |
