Ella is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of 1.975%. If Ella would like to end up with dollar sign, 10, comma, 000$10,000 after 6 years, how much does she need to contribute to the account every quarter, to the nearest dollar? Use the following formula to determine your answer.
The formula to calculate the future value of regular contributions is:
FV = Pmt * ((1 + r)^n - 1) / r
Where:
FV = Future Value ($10,000)
Pmt = Quarterly contribution
r = Quarterly interest rate (1.975% or 0.01975)
n = Number of quarters in 6 years (24 quarters)
Plugging in the values, we get:
$10,000 = Pmt * ((1 + 0.01975)^24 - 1) / 0.01975
$10,000 = Pmt * (1.5519 - 1) / 0.01975
$10,000 = Pmt * 55.32
Pmt = $10,000 / 55.32
Pmt = $180.85
Therefore, Ella needs to contribute approximately $180.85 to the account every quarter to end up with $10,000 after 6 years.