5.32 Maintenance money for a new building has been sought. Mr. Kendall would lik

Question

5.32 Maintenance money for a new building has been sought. Mr. Kendall would like to make a donation to cover all future expected maintenance costs for the building. These maintenance costs are expected to be $100,000 each year for the first five years, $130,000 each year for years 6 through 10, and $150,000 each year after that. (The building has an indefinite service life.) (a) If the money is placed in an account that will pay 13% interest compounded annually, how large should the gift be? (b) What is the equivalent annual maintenance cost over the infinite service life of the building?

Explanation / Answer

a)

interest rate = 13%

Donation = PV

PV = 100000/1.13 + .... + 100000/1.135 + 130000/1.136 + .... + 130000/1.1310 +  (150000/0.13)/1.1310

PV = $939804.3

b)

Equivalent maintenance cost (annual) = y

y/1.13 + y/1.132...... = 939804.3

y = 0.13 x 939804.3

y = $122174.6

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