, nme: Hours rroblem 25points):Youhave beennegotiatinga5 year loan with a bank.

Question

, nme: Hours rroblem 25points):Youhave beennegotiatinga5 year loan with a bank. Based on 10% interest rate, the bank officer has proposed that you pay nothing during the first year, but then pay four equal payments at the end of the 2d, 3nd, 4, and 5h year in the amount of 30,000 dirham each. You have asked the officer to give you another proposal, but with three equal payments starting from end of the 3d year (30, 4th, and 5h. How much would the three payments be so that the second proposal is equivalent to the first. (hints:for both proposals to be equivalent, their equivalent worths (PW. FW, etc.) must be the same

Explanation / Answer

The idea is to compute time value of given cash flows from both streams at any point of time and make them equal.

Find present value of 1st steam:

PV = 30,000/1.1^2 + 30,000/1.1^3 + 30,000/1.1^4 + 30,000/1.1^5

PV = 30,000(1/1.1^2 + 1/1.1^3 + 1/1.1^4 + 1/1.1^5) = 86,450.875810

Find present value of 2nd stream:

PV = PMT(1/1.1^3 + 1/1.1^4 + 1/1.1^5) = 2.055250 PMT

Now, both PVs must be equal as given in question

2.055250 PMT = 86,450.875810

PMT = $42,063.44

Therefore, the three payments be $42,063.44 when both streams are indifferent.

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