Maintenance money for an athletic complex has been sought. Mr. Kendall, the Athletic Director, would like to solicit a donation to cover all future expected maintenance costs for the building. These maintenance costs are expected to be $1 million each year for the first five years, $1.3 million each year for years 6 through 10, and $1.5 million each year after that. (The building has an indefinite service life.) If the money is placed in the account that will pay 5% interest compounded annually, how large should the gift be?

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28 May, 20:44

Maintenance money for an athletic complex has been sought. Mr. Kendall, the Athletic Director, would like to solicit a donation to cover all future expected maintenance costs for the building. These maintenance costs are expected to be $1 million each year for the first five years, $1.3 million each year for years 6 through 10, and $1.5 million each year after that. (The building has an indefinite service life.) If the money is placed in the account that will pay 5% interest compounded annually, how large should the gift be?

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Roxie · Answer 1

Total donation = $76,000,000

Explanation:

Giving the following information:

These maintenance costs are expected to be $1 million each year for the first five years, $1.3 million each year for years 6 through 10, and $1.5 million each year after that. The money is placed in the account that will pay a 5% interest compounded annually.

First, we need to calculate the final value of the donation:

We have 3 perpetual annuities.

FV = 1,000,000/0.05 = 20,000,000

FV = 1,300,000/0.05=26,000,000

FV = 1,5000,000/0.05 = 30,000,000

Total donation = $76,000,000