To solve this we are going to use formula for the future value of an ordinary annuity: [tex]FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ][/tex]
where
[tex]FV[/tex] is the future value
[tex]P[/tex] is the periodic payment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]t[/tex] is the number of years
We know from our problem that the periodic payment is $50 and the number of years is 3, so [tex]P=50[/tex] and [tex]t=3[/tex]. To convert the interest rate to decimal form, we are going to divide the rate by 100%
[tex]r= \frac{4}{100} [/tex]
[tex]r=0.04[/tex]
Since the interest is compounded monthly, it is compounded 12 times per year; therefore, [tex]n=12[/tex].
Lets replace the values in our formula:
[tex]FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ][/tex]
[tex]FV=50[ \frac{(1+ \frac{0.04}{12} )^{(12)(3)} -1}{ \frac{0.04}{12} } ][/tex]
[tex]FV=1909.08[/tex]
We can conclude that after 3 years you will have $1909.08 in your account.
