Marques is saving money and plans on making monthly contributions into an account earning an annual interest rate of 9% compounded monthly. If Marques would like to end up with dollar sign, 25, comma, 000$25,000 after 26 months, 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 the monthly contribution Marques needs to make, we first need to calculate the interest rate per period (i) by dividing the annual interest rate by 12 (since it's compounded monthly):
i = 9% / 12 = 0.09 / 12 = 0.0075
Next, we can plug in the values into the formula:
25,000 = d * ((0.0075) * (1 + 0.0075)^26 - 1) / 0.0075
Solving for d:
25,000 = d * (0.0075 * (1.0075)^26 - 1) / 0.0075
25,000 = d * (0.0075 * 1.2075 - 1) / 0.0075
25,000 = d * (0.009113 - 1) / 0.0075
25,000 = d * (-0.990887) / 0.0075
25,000 = d * (-132.11893)
25,000 / (-132.11893) = d
d ≈ -189.07
Since a negative contribution doesn't make sense, there seems to be an error in the calculations. Let me recalculate that for you.