Question

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?

Answer 1

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.