Chloe is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.675%. If Chloe would like to end up with $17,000 after 6 years, how much does she need to contribute to the account every month, to the nearest dollar?
To find out how much Chloe needs to contribute every month, we can use the future value formula for compound interest:
FV = Pmt * [(1 + r)^n - 1] / r
Where:
FV = Future Value ($17,000)
Pmt = Monthly contribution
r = Monthly interest rate (0.675% or 0.00675)
n = Number of months (6 years * 12 months/year = 72 months)
Substitute the values into the formula:
$17,000 = Pmt * [(1 + 0.00675)^72 - 1] / 0.00675
$17,000 = Pmt * [5.78771 - 1] / 0.00675
$17,000 = Pmt * 4.78771 / 0.00675
$17,000 = 709.9 * Pmt
Pmt = $17,000 / 709.9
Pmt ≈ $23.95
Therefore, Chloe needs to contribute approximately $24 every month to end up with $17,000 after 6 years.