A $25,000 strip bond is purchased for $8235 to yield 8% compounded semiannually. What is the remaining time until maturity?
A) 30.53 years
B) 12.50 years
C) 14.16 years
D) 22.28 years
E) 56.63 years

Question

Quizplus · Accepted Answer

The remaining time until maturity can be calculated using the formula for the future value of a single sum: $FV = PV(1 + i)^n$, where $FV$ is the future value, $PV$ is the present value, $i$ is the interest rate per period, and $n$ is the number of periods. Rearranging the formula to solve for $n$, we get $n = \frac{\log(FV/PV)}{\log(1+i)}$. Given that $FV = \$25,000$, $PV = \$8,235$, and the interest rate is 8% compounded semiannually (which means $i = 0.04$), we can calculate $n$, which represents the total number of compounding periods (semiannual periods). Plugging the values into the formula gives $n = \frac{\log(25000/8235)}{\log(1.04)}$, which calculates to approximately 28.32 semiannual periods. Since each period is half a year, the total time in years is $28.32 / 2 = 14.16$ years.

A $25,000 Strip Bond Is Purchased for $8235 to Yield