Question

You are owed payments of $800 due today, $1,000 due in five months and $1,200 due in one year. You have been approached to accept a single payment seven months from now. What amount should you accept in seven months in place of the three payments? Use an interest rate of 9% per annum and 7 months from now as the focal date.

Answer 1

As the focal point occurs in the future for two payments, we use future value formula for that two payments. For last payment focal point occurs in past and hence we have to use present value formula for last payment.

Let the replacement payment in month seven be $ A.

$ 800 x (1+0.09)7/12 + $ 1,000 x (1+0.09)2/12 + $ 1,200 / (1+0.09)5/12 = $ A

$ 800 x (1.09)7/12 + $ 1,000 x (1.09)2/12 + $ 1,200 / (1.09)5/12 = $ A

$ 800 x 1.05155531734398 + $ 1,000 x 1.01446659214166 + $ 1,200 /1.03655982906645 = $ A

$ A = $ 841.244253875187 + $ 1,014.46659214166 + $ 1,157.67557872732

$ A = $ 3,013.386424744167 or $ 3,013.39

In seven month $ 3,013.39 can be accepted in place of three payments.