Ryan is saving money and plans on making monthly contributions into an account earning an annual interest rate of 7.8% compounded monthly. If Ryan would like to end up with dollar sign, 208, comma, 000$208,000 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
To find out how much Ryan needs to contribute every month, we can rearrange the formula for A to solve for d:
d = A / ( (1 + i)^n - 1 / i )
Plugging in the given values:
A = $208,000
i = 7.8%/12 = 0.65% = 0.0065
n = 11 years * 12 months = 132 months
d = $208,000 / ( (1 + 0.0065)^132 - 1 / 0.0065 )
d = $208,000 / ( (1.0065)^132 - 1 / 0.0065 )
d = $208,000 / ( 2.15674 - 1 / 0.0065 )
d = $208,000 / 154.5
d ≈ $1,346
Therefore, Ryan needs to contribute approximately $1,346 every month to end up with $208,000 after 11 years.