Question

Barbara wants to restore her '66 Mustang in 4 years. She puts $200 into an account every month that pays 4.5% interest, compounded monthly. How much is in the account after 4 years?

Answer 1

Answer:

$10496.77

Step-by-step explanation:

We have been given that Barbara puts $200 into an account every month that pays 4.5% interest, compounded monthly.

To find the money in the account after 4 years, we will use future value formula.  

$FV=R(\frac{1+\frac{r}{n})^{nt}-1}{\frac{r}{n}})$, where,

R = Regular deposits,

r = Interest rate in decimal form

n = Number of times interest in compounded per year,

t = Time in years.

$4.5\%=\frac{4.5}{100}=0.045$

Substitute given values:

$FV=\ 200(\frac{1+\frac{0.045}{12})^{12*4}-1}{\frac{0.045}{12}})$

$FV=\ 200(\frac{1+0.00375)^{48}-1}{0.00375})$

$FV=\ 200(\frac{1.00375)^{48}-1}{0.00375})$

$FV=\ 200(1.1968143774194609-1}{0.00375})$

$FV=\ 200(0.1968143774194609}{0.00375})$

$FV=\ 200(52.4838339785229066667)$

$FV=\ 10496.76679570458133334$

$FV\approx \ 10496.77$

Therefore, there will be an amount of $10496.77 in the account after 4 years.