Question

Samantha's retirement fund has an accumulated amount of $35,000. If it has been earning interest at 2.56% compounded monthly for the past 24 years, calculate the size of the equal payments that he deposited at the beginning of every 3 months. Round to the nearest cent

Answer 1

The size of the equal payments that Samantha deposited at the beginning of every 3 months is approximately $75.15.

Step-by-step explanation:

To calculate the size of the equal payments that Samantha deposited at the beginning of every 3 months, we can use the formula for the future value of an ordinary annuity. The formula is FV = P * [(1 + r)^n - 1] / r, where FV is the future value, P is the payment amount, r is the interest rate per period, and n is the number of periods. In this case, FV is $35,000, r is 2.56% divided by 12 to get the monthly rate, and n is 24 years multiplied by 12 to get the number of months. Plugging in these values, we can solve for P.

P = $35,000 / [(1 + 0.0256/12)^(24*12) - 1] / (0.0256/12)

P ≈ $35,000 / 464.975746

P ≈ $75.15.