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%

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 $2.88\%\times 2=5.76\%$ .