Question

Scheduled payments of $1186,$437, and $363 are due in one-and-a-half years, four years, and five years respectively. What is the equivalent single replacement payment two years from now if interest is 8.9% compounded annually? The equivalent single replacement payment is $ (Round the fintal answer to the nearest cent as needed. Round all intermediate values to six decimal places: as needed.)

Answer 1

The question requires calculating the equivalent single payment due in two years for three scheduled payments, factoring in compound interest. The procedure involves discounting the scheduled payments back to their present value as of two years from now, then summing them to find the total replacement payment.

Step-by-step explanation:

The question involves finding the equivalent single replacement payment due two years from now for three different payments scheduled at different times in the future, given an interest rate of 8.9% compounded annually. We need to calculate the present value of each individual payment as if it were to be paid two years from now, using the formula for the present value of a future payment, which is Present Value = Future Payment / (1 + r)^n, where r is the interest rate and n is the number of periods until the payment is due.

• First payment: $1186 due in 1.5 years, thus n = 1.5-2 = -0.5 years.
  
• Second payment: $437 due in 4 years, thus n = 4-2 = 2 years.
  
• Third payment: $363 due in 5 years, thus n = 5-2 = 3 years.
  

After calculating the present value of each payment at the two-year mark, sum these values to get the total equivalent single replacement payment.