Question

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?

Decimals
ANSWERED
asked 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 \(9\%\) annual rate compounded
a) Annually?
b) Continuously?

Answers (1)

2021-05-18
Step 1
First we write the formula \(A= \text{Final amount}\ P= \text{principal amount}\ r= \text{rate of interest}\) (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 \(A= $1200,\)
\(r= 9\%=0.09,\ n =1\) and \(t=10\) years
\(12000=P\left(1+\frac{0.09}{1}\right)^{1\times10}\)
\(12000=P(1.09)^{10}\)
\(12000=P\times2.37\)
\(P=\frac{12000}{2.37}=$5063.29\)
Step 3
Answer: \($5063.29\) to be invested to get the final amount \($12000\) after 10 years compounded annually.
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