Question

Suppose you invest $50 a month in an annuity that earns 4% APR compounded monthly. How much money will you have in this account after 3 years?

Answer 1

To solve this we are going to use formula for the future value of an ordinary annuity: $FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]$
where
$FV$ is the future value
$P$ is the periodic payment
$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year
$t$ is the number of years

We know from our problem that the periodic payment is $50 and the number of years is 3, so $P=50$ and $t=3$. To convert the interest rate to decimal form, we are going to divide the rate by 100%
$r= \frac{4}{100}$
$r=0.04$
Since the interest is compounded monthly, it is compounded 12 times per year; therefore, $n=12$.
Lets replace the values in our formula:
$FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]$
$FV=50[ \frac{(1+ \frac{0.04}{12} )^{(12)(3)} -1}{ \frac{0.04}{12} } ]$
$FV=1909.08$

We can conclude that after 3 years you will have $1909.08 in your account.

Answer 2

Answer:

APEX answer is $1909.08