Help- can anybody explain to me how to solve problem 4-3 fromEngineering Economi

Question

Help- can anybody explain to me how to solve problem 4-3 fromEngineering Economic Analysis 10th Ed. by Donald G. Newnan, J.P.Lavelle, and T.G. Eschenbach? Problem states : For what value of n, bas ed on a 3.5% intrestdo the depectied cash flows have a value of zero.                               A=50                 1-2-3--4-5-6--7-8-9-........n -1000 Sure answer is simple but darn if I can figure it out. By the way anybody have or know where to get the solutionmanual for this book for free? Help- can anybody explain to me how to solve problem 4-3 fromEngineering Economic Analysis 10th Ed. by Donald G. Newnan, J.P.Lavelle, and T.G. Eschenbach? Problem states : For what value of n, bas ed on a 3.5% intrestdo the depectied cash flows have a value of zero.                               A=50                 1-2-3--4-5-6--7-8-9-........n -1000 Sure answer is simple but darn if I can figure it out. By the way anybody have or know where to get the solutionmanual for this book for free?

Explanation / Answer

First, we have a payment of 1000 dollars in period 1. Thishas a PV of -1000 / 1.035 = -966.18. Then we have an annuity of n periods. However, this annuityis delayed by 1 year (first payment is in period 2, not 1) and thuswe have to discount the annuity formula by 1 period. Therefore, the PV of the annuity is 1/(1+r) * [A/r * (1 - 1/(1+r)^n)] = 1/1.035 * 50/.035 * (1 -1/(1.035)^n) Setting this equal to 966.18 and solving for n, we get n = 35years.

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