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.

Answer 1

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.