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 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? 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.