# You want to invest money for your child's education in a certificate of deposit (CD). You want it to be worth \$12,000 in 10 years. How much should you invest if the CD pays interest at a 9\% annual rate compounded a) Annually? b) Continuously?

Dottie Parra 2021-05-17 Answered
You want to invest money for your child's education in a certificate of deposit (CD). You want it to be worth $12,000$ in 10 years. How much should you invest if the CD pays interest at a $9\mathrm{%}$ annual rate compounded
a) Annually?
b) Continuously?
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Step 1
First we write the formula (in decimals)
$n=$number of times principal amount compounded in a year and $t=$ period of investment
$A=P{\left(1+\frac{r}{n}\right)}^{nt}$
Step 2
Now we put the values $A=1200,$
and $t=10$ years
$12000=P{\left(1+\frac{0.09}{1}\right)}^{1×10}$
$12000=P\left(1.09{\right)}^{10}$
$12000=P×2.37$
$P=\frac{12000}{2.37}=5063.29$
Step 3
Answer: $5063.29$ to be invested to get the final amount $12000$ after 10 years compounded annually.