Jeriel deposits dollar sign, 270$270 every month into an account earning an annual interest rate of 7.8% compounded monthly. How much would he have in the account after 24 months, to the nearest dollar? Use the following formula to determine your answer.
The formula to calculate the future value of an account with regular monthly deposits is:
FV = Pmt * (((1 + r/n)^(nt) - 1) / (r/n)) + Pmt * (1 + r/n)^(nt)
Where:
FV = Future value of the account
Pmt = Monthly deposit amount ($270)
r = Annual interest rate (7.8% or 0.078)
n = Number of compounding periods per year (12 for monthly compounding)
t = Number of years (24 months / 12 months per year = 2 years)
Plugging in the values:
FV = $270 * (((1 + 0.078/12)^(12*2) - 1) / (0.078/12)) + $270 * (1 + 0.078/12)^(12*2)
FV = $270 * (((1 + 0.0065)^(24) - 1) / 0.0065) + $270 * (1.0065)^(24)
FV = $270 * ((1.0065^(24) - 1) / 0.0065) + $270 * 1.170178
FV = $270 * ((1.172003 - 1) / 0.0065) + $316.8534
FV = $270 * (0.172003 / 0.0065) + $316.8534
FV = $270 * 26.4625 + $316.8534
FV = $7,133.7750 + $316.8534
FV = $7,450.63
Therefore, Jeriel would have approximately $7,450 in the account after 24 months.