Chapter 5, Problem 50RE

Funding a College Education A child's grandparents purchase a $\$10,000$ bond fund that matures in 18 years to be used for her college education. The bond fund pays $4\%$ interest compounded semiannually. How much will the bond fund be worth at maturity? What is the effective rate of interest? How long will it take the bond to double in value under these terms?

To determine

To find: How much will the bond fund be worth at maturity? What is the effective rate of interest? How long will it take the bond to double in value under these terms?

Answer to Problem 50RE

$20,398.87,0.04\%$ and $17.5$.

Explanation of Solution

Given:

Using the compound interest.

$P=10000$

$r=0.04$

$t=18$

Calculation:

$A=P{\left(1+\frac{r}{2}\right)}^{2t}$

$A=10000{\left(1+\frac{0.04}{2}\right)}^{2\left(18\right)}=20,398.87$

Rate of interest is $0.04\%$. Then,

$A=P{\left(1+\frac{r}{2}\right)}^{2t}$

$20000=10000{\left(1+\frac{0.04}{2}\right)}^{2t}$

$2={\left(1+\frac{0.04}{2}\right)}^{2t}\Rightarrow t=17.5$