Final answer:
The question requires calculating the equivalent single replacement payment for three scheduled future payments when considering an annual compound interest rate of 8.5%. By finding the present value of each scheduled payment and then determining their future values three years from now at the same interest rate, we arrive at the single payment amount needed.
Step-by-step explanation:
The task at hand is to calculate the equivalent single replacement payment three years from now, for scheduled payments of $1098, $1112, and $1084 due in one-and-a-half years, four-and-a-half years, and five-and-a-half years respectively, considering an interest rate of 8.5% compounded annually. To solve this, we must first find the present value of each payment as of the payment date, and then calculate what single sum of money would need to be put aside three years from now at the same 8.5% interest rate so that it grows to equal the total present value of the three payments when they are due.
To find the present value (PV) of each payment, we use the formula PV = FV / (1 + r)^n, where FV is the future value or the scheduled payment amount, r is the annual interest rate (expressed as a decimal), and n is the number of years until the payment is due. Then, we find the future value of these present values as of three years from now using the formula FV = PV × (1 + r)^n. The sum of these future values will give us the equivalent single replacement payment that would need to be made three years from today.