April wants to create a scholarship fund by making annual savings donations to t

Question

April wants to create a scholarship fund by making annual savings donations to the fund for several years before the fund starts making annual scholarship payments forever. She plans to save 12,700 dollars per year in the trust fund for 3 years. Her first savings donation to the trust fund is expected later today. How much can the trust fund be expected to provide each year for scholarships if the fund is expected to earn 3.96 percent per year, make equal, fixed scholarship payments forever, and make its first scholarship payment in 4 years from today?

Explanation / Answer

Value of annual deposites by April at the begining of year 4:
Formula: FV = Pmt x ((1+r)n -1))/r)

FV = $12,700 x ((1+0.0396)3 -1))/0.0396) = $39,628.68

Fixed Scholarship per year:
Formula: PV of perpetuity = Anuuity payments / Interest rate
=> $39,628.68 = Perpetual Annuity Payments / 0.0396
=> Perpetual Annuity Payments = $39,628.68 x 0.0396 = $1,569.30

So, the trust fund is expected to provide $1,569.30 every year.

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