A 60 year old alum donates 300000 today (at t-0) to the College for an annual...

A 60 year old alum donates 300000 today (at t-0) to the College for an annual scholarship that will start with the first scholarship payment in t=20, and thereafter, the scholarship amount will grow at a rate of 3% / year to account for inflation. If the College's discount rate is 7%%, how large will the first payment in t=20 be??

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Expert Solution

Donation today = 300,000

Discount Rate, r = 7%

Value of Donation after 20 years (at t=20) = 300,000*(1+7%)²⁰ = 1,160,905.34 ---------------(1)

Let D be the first scholarship amount

Growth rate of scholarship, g = 3%

The scholarship will be given for perpetuity

The present value of growing perpetuity at t=20, PV = D/(r-g) = D/(7%-3%) = D/0.04 -----------------(2)

Equating equations (1) and (2)

1,160,905.34 = D/0.04

D = 0.04 X 1,160,905.34 = 46,436.21

The first scholarship payment at t=20 will be 46,436.21

jeff jeffy answered 2 years ago

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