Kiran is saving money and plans on making monthly contributions into an account earning an annual interest rate of 4.2% compounded monthly. If Kiran would like to end up with dollar sign, 89, comma, 000$89,000 after 11 years, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
A, equals, d, left bracket, start fraction, left bracket, 1, plus, i, right bracket, to the power n , minus, 1, divided by, i, end fraction, right bracket
A=d(
i
(1+i)
n
−1
)
A, equalsA= 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
In this case,
A = $89,000
i = 4.2%/12 = 0.35% = 0.0035
n = 11 years * 12 months/year = 132
Plugging these values into the formula:
$89,000 = d(0.0035(1+0.0035)^132 - 1) / 0.0035
Solving for d:
$89,000 = d(179.4696 - 1) / 0.0035
$89,000 = 178.4696d / 0.0035
$89,000 * 0.0035 = 178.4696d
$311.50 = 178.4696d
d = $311.50 / 178.4696
d ≈ $174.57
Therefore, Kiran needs to contribute approximately $174.57 every month to the account to end up with $89,000 after 11 years.