Seventeen years after it was first issued at 11% compounded semi-annually, a 30-year, $1,000 strip bond was sold on the bond market at a price that would provide the purchaser with a yield rate of 6.4% compounded semi-annually. What was the selling price at that time?
A) $440.89
B) $342.68
C) $248.56
D) $161.96
E) $103.78

Question

Quizplus · Accepted Answer

The selling price of the bond can be calculated using the formula for the future value of a present amount at compound interest: $P = P_0(1 + r)^n$, where $P$ is the future value, $P_0$ is the present value (initial investment), $r$ is the interest rate per period, and $n$ is the number of periods. Since the bond is a zero-coupon bond (strip bond), it pays no interest until maturity. The buyer is interested in a yield rate of 6.4% compounded semi-annually for the remaining 13 years (26 periods) of the bond's life. The future value of the bond at maturity (in 13 years) is its face value, $1,000. We rearrange the formula to solve for $P_0$, the present value or selling price: $P_0 = \frac{P}{(1 + r)^n}$. Substituting $P = $1,000$, $r = 0.032$ (6.4% per annum compounded semi-annually gives 3.2% per period), and $n = 26$, we get $P_0 = \frac{1000}{(1 + 0.032)^{26}}$, which calculates to approximately $440.89.

Seventeen Years After It Was First Issued at 11% Compounded