Omar is saving money and plans on making monthly contributions into an account earning an annual interest rate of 3.9% compounded monthly. If Omar would like to end up with dollar sign, 10, comma, 000$10,000 after 17 months, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
The formula to calculate the monthly contribution needed to reach the desired amount is:
PMT = A / (((1 + r)^n - 1) / r)
Where:
PMT = monthly contribution
A = desired amount ($10,000)
r = monthly interest rate (3.9% annual rate divided by 12 months = 0.325% or 0.00325 as a decimal)
n = number of months (17)
Plugging in the values:
PMT = $10,000 / (((1 + 0.00325)^17 - 1) / 0.00325)
PMT = $10,000 / (((1.00325)^17 - 1) / 0.00325)
PMT = $10,000 / ((1.055465 - 1) / 0.00325)
PMT = $10,000 / (0.055465 / 0.00325)
PMT = $10,000 / 17.053846
PMT ≈ $587.42
Therefore, Omar needs to contribute approximately $587 every month to reach a total of $10,000 after 17 months.