Final answer:
To have $500,000 after 25 years with 4% compounded monthly interest, Carol needs to put approximately $1,457.25 into her credit union.
Step-by-step explanation:
To calculate the amount of money Carol needs to put into her credit union to have $500,000 after 25 years with 4% compounded monthly interest, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)
Where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, P is unknown, FV is $500,000, r is 4% (0.04), n is 12 (compounded monthly), and t is 25. Plugging in these values:
$500,000 = P * [(1 + 0.04/12)^(12*25) - 1] / (0.04/12)
Solving for P, we get:
P = $500,000 * (0.04/12) / [(1 + 0.04/12)^(12*25) - 1]
P ≈ $1,457.25