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.

Answer 1

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.