Question

Scheduled payments of $898, $967, and $617 are due in one year, three-and-a-half years, and five-and-a-half years respectively. What is the equivalent single replacement payment two years from now if interest is 6.8% compounded semi-annually?

The equivalent single replacement payment is $__.

Answer 1

Determine the present value of the three scheduled payments for the equivalent single replacement payment two years from now. The value is $1994.59.

Step-by-step explanation:

To find the equivalent single replacement payment two years from now, we need to calculate the present value of the three scheduled payments. Using the formula for compound interest:

PV = PMT / (1 + r/2)n

Where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

Plugging in the values:

PV1 = $898 / (1 + 0.068/2)2 = $818.50

PV2 = $967 / (1 + 0.068/2)7 = $748.69

PV3 = $617 / (1 + 0.068/2)11 = $427.40

Finally, we can calculate the equivalent single replacement payment two years from now:

PV = PV1 + PV2 + PV3 = $818.50 + $748.69 + $427.40 = $1994.59