Question

You are setting up a trust fund to give engineering students scholarships forever, and should be able to get 5% interest on the fund. You would like to:

Provide 1 student with a $2,000 scholarship EACH YEAR

Provide an additional student with a $5,000 scholarship every four years, STARTING IN YEAR FOUR.

a.Draw the cash flow diagram for the problem – include 4 years in the diagram (one cycle).

b. How much money needs to be in the trust fund today to financially support the scholarship fund forever?

Answer 1

a.

Year 1	Year 2	Year 3	Year 4
2000	2000	2000	2000+5000 = 7000

b.

The money required today will be the present value of all the future cash flows. The future cash flow is two infinite GP series:

Yearly - 2000, 2000, 2000, 2000, ................... till infinite

Every 4th Year - 5000, 5000, 5000, ............... till infinite

So finding the PV = PV of the first series and PV of the second series

interest rate = 5%

PV = (2000/(1.05) + 2000/(1.05^2) + 2000/(1.05^3) + 2000/(1.05^4) .............) + (5000/(1.05^4) + 5000/(1.05^8) + 5000/(1.05^12) ..........)

PV = (2000/1.05)/(1 - (1/1.05)) + (5000/1.05^4)/(1 - (1/1.05^4)) = $63,201.183