Chapter 5.7, Problem 64AYU

Problems 63-66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made.

Zero-Coupon Bonds A child’s grandparents are considering buying a $\$80,000$ face-value, zero-coupon bond at birth so that she will have money for her college education 17 years later. If they want a rate of return of $6\%$ compounded annually, what should they pay for the bond?

To determine

To find: Bonds A child’s grandparents are considering buying a $\$80,000$ face-value, zero-coupon bond at birth so that she will have money for her college education 17 years later. If they want a rate of return of $6\%$ compounded annually, what should they pay for the bond?

Answer to Problem 64AYU

Solution:

$\$29709.15$

Explanation of Solution

Given:

$A=\$80,000 r=6\%=0.06$ and $t=17$

Calculation:

$6\%$ interest compounded annually

$P=A{\left(1+\frac{r}{n}\right)}^{-nt}$

$P=80000{\left(1+\frac{0.06}{1}\right)}^{-1\left(17\right)}$

$=29709.15$

Now, they want to pay $\$29709.15$.