Marques deposits $320 every month into an account earning an annual interest rate of 4.5% compounded monthly. How much would he have in the account after 29 months, to the nearest dollar?

A formula can be used to calculate the value of an account that grows off of compound interest when recurring payments are made (assuming) at the end of each month.

[tex]FV = P \times \dfrac{\left(1+\dfrac{r}{n}\right)^{nt}-1}{\dfrac{r}{n}}[/tex]

where

P is the value of the recurring payments
r is the rate of the compound interest (decimal form)
n is the number of times interest is compounded per year
t is the time that elapses in years
FV is the value of the account after t years.

[tex]\hrulefill[/tex]

Solving the Problem

We're told

r = 0.045 (4.5%)
P = $320
the payments are made on a monthly basis
t= 29/12
n = 12

So,

[tex]FV = (320) \times \dfrac{\left(1+\dfrac{0.045}{12}\right)^{(12)(\frac{29}{12}) }-1}{\dfrac{0.045}{12}}[/tex]

[tex]FV = 9784[/tex]

.