Seven years before it matures the value of a $1,000 strip bond is $672. What is the semi-annually compounded nominal interest rate?
A) 5.76%
B) 5.84%
C) 3.10%
D) 24.40%
E) 2.88%

Question

Quizplus · Accepted Answer

The value of a strip bond can be calculated using the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods. Here, $PV = $672$, $FV = $1,000$, and $n = 7 \times 2 = 14$ periods (since the interest is compounded semi-annually). Rearranging the formula to solve for r gives us $r = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1$. Plugging in the values gives $r = \left(\frac{1000}{672}\right)^{\frac{1}{14}} - 1 \approx 0.0288$ per period, or $2.88\%$ per semi-annual period. Since the nominal annual interest rate is the semi-annual rate multiplied by 2, the nominal annual interest rate is $2.88\% \times 2 = 5.76\%$.

Seven Years Before It Matures the Value of a $1,000