Answer:
To find the payment made at the end of each six months that will accumulate to $10,500 at 9% compounded annually, we can use the future value of an annuity formula.
Given:
Future Value (FV) = $10,500
Interest Rate (r) = 9% per year, compounded annually
Number of periods (n) = 7 years (or 14 six-month periods)
Using the formula for future value of an annuity:
FV = Payment * [(1 + r)^n - 1] / r
Rearranging the formula to solve for the payment:
Payment = FV * r / [(1 + r)^n - 1]
Plugging in the given values:
Payment = $10,500 * 0.09 / [(1 + 0.09)^14 - 1]
Calculating the payment:
Payment ≈ $536.69
Therefore, a payment of approximately $536.69 made at the end of each six months for 7 years will accumulate to $10,500 at 9% compounded annually.