Gianna is saving money and plans on making monthly contributions into an account earning an annual interest rate of 3% compounded monthly. If Gianna would like to end up with$26,000 after 3 years, how much does she need to contribute to the account every month, to the nearest dollar?
To calculate the monthly contribution Gianna needs to make, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money Gianna wants to end up with ($26,000)
P = the monthly contribution
r = annual interest rate (3% or 0.03)
n = number of times the interest is compounded per year (12 for monthly)
t = number of years (3)
Plugging in the values, we get:
26,000 = P(1 + 0.03/12)^(12*3)
26,000 = P(1 + 0.0025)^36
26,000 = P(1.0025)^36
26,000 = P(1.110378)
P = 26,000 / 1.110378
P ≈ $23,429.35
Therefore, Gianna needs to contribute approximately $23,429 every month to end up with $26,000 after 3 years.