Assume that a grateful engineering economy graduate starts an endowment at Calif

Question

Assume that a grateful engineering economy graduate starts an endowment at Californa University by donating $100,000 now. The conditions of the donation are that scholarships totaling $10,000 per year are to be given to engineering economy students beginning now and continuing through year 5. After that (i.e., year 6), scholarships are to be given in an amount equal to the interest that is generated on the investment. If the investment earns an effective rate of 10% per year, compounded continuously, how much money will be available for scholarships from year 6 on?

Explanation / Answer

ans....
If $ 10,000 scholarship is given now, the value of the endowment now equals $ 90,000
The value of the endowment at end of year 1 = $ 90,000 e(0.10 x 1) - $ 10,000
The value of the endowment at end of year 1 = $ 99,465.38 - $ 10,000
The value of the endowment at year 1 end = $ 99,465.38 - $ 10,0000
The value of the endowment at year 1 end = $ 89,465.38
The value of the endowment at end of year 2 = $ 89,465.38 e(0.10 x 1) - $ 10,000
The value of the endowment at end of year 2 = $ 88,874.53
The value of the endowment at end of year 3 = $ 88,874.53 e(0.10 x 1) - $ 10,000
The value of the endowment at end of year 3 = $ 88,221.53
The value of the endowment at end of year 4 = $ 88,221.53 e(0.10 x 1) - $ 10,000
The value of the endowment at end of year 4 = $87,499.87
The value of the endowment at end of year 5 = $ 87,499.87 e(0.10 x 1) - $ 10,000
The value of the endowment at end of year 5 = $86,702.30
The scholarship available from year 6 onwards equals the interest earned on the endowment from year 5
The interest earned on the endowment on year 5 = $86,702.30 x e 0.10 x 1
The interest earned on the endowment on year 5 =10,000

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