Question

A child’s grandparents wish to purchase a bond that matures in 18 years to be used for her college education. The bond pays 4% interest compounded semiannually. How much should they pay so that the bond will be worth $85,000 at maturity?

Short answer

The amount to be paid for the bond to be worth $\$85000$at maturity is :$\$41668.97$

Step-by-step solution

Step 1. Given information  

A child’s grandparents wish to purchase a bond that matures in 18 years to be used for her college education. The bond pays 4% interest compounded semiannually.

Step 2. Required to find  

How much should they pay so that the bond will be worth $85,000 at maturity?

Step 3. Finding the amount to be paid for the bond to be worth $85000at maturity

Using the compound interest formula, $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Put $A=85000,r=0.04,n=2,t=18$

$85000=P{\left(1+\frac{0.04}{2}\right)}^{2\times 18}$

$\Rightarrow 85000=P{\left(1+0.02\right)}^{36}$

$\Rightarrow 85000=P{\left(1.02\right)}^{36}$

$\Rightarrow \frac{85000}{1.{02}^{36}}=P$

$\Rightarrow P=\frac{85000}{2.0398}$

$\Rightarrow P=41668.97$