For a homeowner's association to accumulate $50,000 in eight years at 3.75% interest, what will be the quarterly payment?

To determine the quarterly payment required for a homeowner's association to accumulate $50,000 in eight years at an interest rate of 3.75%, it's essential to understand that this scenario describes a future value of an annuity problem. You can use the future value of an annuity formula, which accounts for regular payments made over time along with interest compounding.

The future value of an annuity formula can be expressed as:

[ FV = P \times \frac{(1 + r)^n - 1}{r} ]

Where:

• FV is the future value of the annuity ($50,000 in this case).

• P is the payment amount (what we want to find).

• r is the interest rate per period (annual interest rate divided by the number of compounding periods per year).

• n is the total number of payments (number of years multiplied by the number of compounding periods per year).

In this scenario:

• The annual interest rate is 3.75%, so the quarterly interest rate will be ( \frac{3.75%}{4} = 0.9375% = 0.009375 ) as a decimal.

• The total number of payments over eight