Nadia wants to establish a charitable foundation that will make annual scholarsh

Question

Nadia wants to establish a charitable foundation that will make annual scholarship payments of $50,700 per year forever. Nadia wants the foundation to make the first annual $50,700 scholarship payment in 10 years from today and she wants annual scholarship payments of $50,700 to continue forever. To fund the foundation, Nadia plans to make equal annual donations to the foundation for 9 years. How much does Nadia need to donate to the foundation each year for 9 years to have exactly enough in the foundation if she makes her first donation to the foundation in one year from today, all donations to the foundation are equal, and funds held by the foundation are expected to earn 12.60 percent per year?

Explanation / Answer

PV of perpetuity at end of 9 year = amount/r

= 50700/.126

= $ 402380.95

PV of perpetutiy = 402380.95/(1.126)^9

= $138290.36

Now we use this value in PV of annuity formula to find amount of donation

138290.36 = payment * (1 - (1+r)^-n)/r

payment = $26548.92

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