Question

2. (20points). Harry just deposited $1500 into a savings account earning 8% interest compoundedmonthlya) How much will be in the account after ten years?b) How much interest will you earn?c) How much will much will you deposit into an account now in order to have $6000 in theaccount in 8 years. Assume the account earns interest rate of 8% compounded monthly

Answer 1

Compound Interest Formula

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

FV = future value of the deposit

P = principal or amount of money deposited

r = annual interest rate (in decimal form)

n = number of times compounded per year

t = time

a) How much will be in the account after ten years?

$\begin{gathered} FV=1500\cdot(1+\frac{0.08}{12})^{12\cdot10} \\ FV=3329.46 \end{gathered}$

b) How much interest will you earn?

$3329.46-1500=1829.46$

c) How much will much will you deposit into an account now in order to have $6000 in the

account in 8 years. Assume the account earns interest rate of 8% compounded monthly

$\begin{gathered} 6000=D\cdot(1+\frac{0.08}{12})^{12\cdot8} \\ 6000=D\cdot(1+\frac{0.08}{12})^{96} \\ 6000=D\cdot1.8925 \\ D=\frac{6000}{1.8925}=3170.41 \end{gathered}$