# Present value of a treasury bond and yield to maturity problem

A treasury bond makes semi-annual payments of $300 for 10 years. At the end of 10 years, the bonds principal amount of $10,000 is paid to the investor.

(a) What is the present value of the bond if the annual interest rate is 5%?

(b) Suppose the bond is observed trading at $11,240. What discount rate are investors using to value the bonds cash flows?

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#### Solution Preview

(a)

Here the investor receives 20 $300 payments at 6-month intervals.

PV bond = PV semiannual payments + PV principal payment

300 x [1/(0,05/2)] x [1- 1/(1+0,05/2)20 ...

#### Solution Summary

PV of bond is calculated after finding the semiannual rate. Then yield to maturity is calculated.

$2.19