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?

A) $17.25
B) $18.85
C) $20.50
D) $21.20
E) $23.50

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.