Question

Scheduled payments of ​$1095​, ​$678​, and​$417are due in one-and-a-half years​ four-and-a-half ​years, and six years respectively. What is the equivalent single replacement payment two-and-a-half years from now if interest is9% compounded annually?

Answer 1

The question involves calculating the equivalent single replacement payment of three differently scheduled payments due in the future, considering the effects of compound interest. The present value formula for compound interest is applied to each future payment to determine their values two-and-a-half years from now.

Step-by-step explanation:

The calculation involves finding the present value of each scheduled payment and then calculate their sum to find the equivalent single replacement payment two-and-a-half years from now, considering a 9% annual compound interest rate. For each scheduled payment, we will use the present value formula for compound interest:

PV = FV / (1 + r)n

where PV represents present value, FV is the future value of the payment, r is the annual interest rate (expressed as a decimal), and n is the number of periods until the payment is made.

Let's calculate the present value for each payment:

1. PV of the first payment due in 1.5 years: $1095 / (1 + 0.09)1.5-0.5
2. PV of the second payment due in 4.5 years: $678 / (1 + 0.09)4.5-0.5
3. PV of the third payment due in 6 years: $417 / (1 + 0.09)6-0.5

Finally, we add all calculated present values to find the equivalent single replacement payment.