Dottie Parra

2021-05-17

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?

a) Annually?

b) Continuously?

comentezq

Skilled2021-05-18Added 106 answers

Step 1

First we write the formula $A=\text{Final amount}\text{}P=\text{principal amount}\text{}r=\text{rate of interest}$ (in decimals)

$n=$number of times principal amount compounded in a year and $t=$ period of investment

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

Step 2

Now we put the values $A=\$1200,$

$r=9\mathrm{\%}=0.09,\text{}n=1$ and $t=10$ years

$12000=P{(1+\frac{0.09}{1})}^{1\times 10}$

$12000=P(1.09{)}^{10}$

$12000=P\times 2.37$

$P=\frac{12000}{2.37}=\$5063.29$

Step 3

Answer: $\$5063.29$ to be invested to get the final amount $\$12000$ after 10 years compounded annually.

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