Chapter 5.7, Problem 66AYU

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 If Pat pays $\$15,334.65$ for a $\$25,000$ face-value, zero-coupon bond that matures in 8 years, what is his annual rate of return?

To determine

To find: Zero-Coupon Bonds If Pat pays $\$15,334.65$ for a $\$25,000$ face-value, zero-coupon bond that matures in 8 years, what is his annual rate of return?

Answer to Problem 66AYU

Solution:

$r=6.3\%$

Explanation of Solution

Given:

$A=\$25,000, P=15334.65$ and $t=8$

Calculation:

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

$25000=15334.65 {\left(1+\frac{r}{1}\right)}^{1\left(8\right)}$

$\frac{25000}{15334.65}= {\left(1+r\right)}^8$

$1.63030={\left(1+r\right)}^8$

$1+r={\left(1.63030\right)}^{\frac{1}{8}}$

$1+r=1.063$

$r=0.063$

$r=6.3\%$

The annual rate of return is $6.3\%$.