Question

You are offered a court settlement in the following terms: you will receive 7 equal payments...

You are offered a court settlement in the following terms: you will receive 7 equal payments of $765 each every year, with the first payment being made 2 years from now. The current annual interest rate is 3%. Assume yearly compounding. What is this settlement worth in present value terms? Enter your answer in the form of dollars, rounded to the nearest cent, and without the dollar sign ('$').

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Answer #1

Formula to compute total PV of cash flows is:

PV = C1/ (1+r) + C2/ (1+r) 2 + …..+ C n/ (1+r) n

C1, C2 … C n is cash flow in year 1, 2, n etc.

Substituting the cash flows and value of r and solving, we get PV as:

PV = 0 + $ 765/ (1+0.03)2 + $ 765/ (1+0.03)3 + $ 765/ (1+0.03)4 +$ 765/ (1+0.03)5 +$ 765/ (1+0.03)6 +$ 765/ (1+0.03)7 + 765/ (1+0.03)8

= $ 765/ (1.03)2 + $ 765/ (1.03)3 + $ 765/ (1.03)4 +$ 765/ (1.03)5 +$ 765/ (1.03)6 +$ 765/ (1.03)7 + 765/ (1.03)8

= $ 765/ 1.0609 + $ 765/ 1.092727 + $ 765/ 1.12550881 +$ 765/ 1.1592740743 +$ 765/ 1.194052296529 +$ 765/ 1.22987386542487 + 765/ 1.26677008138762

= $ 721.085870487322 + $ 700.083369405167 + $ 679.692591655502 + $ 659.895720053885 + $ 640.675456362996 + $ 622.015006177666 + $ 603.898064250161

= $ 4,627.346078392699 or $ 4,627.35

Settlement worth in present value is 4,627.35

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