A zero-coupon bond with a face value of $1,000 is issued at an initial price of $375. The bond matures in 20 years. What is the implicit interest, in dollars, for the first year of the bond's life?

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Quizplus · Accepted Answer

The implicit interest for the first year can be calculated by finding the interest rate and then applying it to the initial price. The formula for the future value of a present amount at compound interest is $FV = PV(1 + r)^n$, where $FV$ is the future value, $PV$ is the present value, $r$ is the annual interest rate, and $n$ is the number of years. Rearranging the formula to solve for $r$, we get $r = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1$. Plugging in the given values ($FV = \$1000$, $PV = \$375$, $n = 20$), we find $r$. Then, the implicit interest for the first year is the initial price (\$375) times the rate ($r$). Given: $FV = \$1000$, $PV = \$375$, $n = 20$First, find $r$: $r = \left(\frac{1000}{375}\right)^{\frac{1}{20}} - 1 \approx 0.0502$ or $5.02\%$Then, calculate the first year's interest: $375 \times 0.0502 \approx \$18.825$Rounded to the nearest cent, the implicit interest for the first year is approximately \$18.85.

A Zero-Coupon Bond with a Face Value of $1,000 Is