Keilantra is saving money and plans on making quarterly contributions into an account earning an annual interest rate of 3.2% compounded quarterly. If Keilantra would like to end up with dollar sign, 61, comma, 000$61,000 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.
A= the future value of the account after n periods
d, equalsd= the amount invested at the end of each period
i, equalsi= the interest rate per period
n, equalsn= the number of periods
To find out how much Keilantra needs to contribute every quarter, we can use the formula for compound interest:
A = d * ((1 + i)^n - 1) / i
Given:
A = $61,000
i = 3.2% = 0.032 (annual interest rate compounded quarterly)
n = 4*6 = 24 quarters
We need to find out the quarterly contribution amount, d.
$61,000 = d * ((1 + 0.032)^24 - 1) / 0.032
$61,000 = d * (1.032^24 - 1) / 0.032
$61,000 = d * (1.91054 - 1) / 0.032
$61,000 = d * 0.91054 / 0.032
$61,000 = 28.517*d
d = $61,000 / 28.517
d ≈ $2,137
Therefore, Keilantra needs to contribute approximately $2,137 every quarter to end up with $61,000 after 6 years.