Question

maintenance money for an athletic complex has been sought by Mr Kendall the athletic director he would like to solicit a donation to cover all future expected maintenance costs for the building. these maintenance costs are expected to be 1.4 million each year for the first 5 years 1.7 million each year for year 6 through 10 and 1.9 million each year after that The building has an indefinite service life if the money is placed into account they will pay 7% interest compounded annually how large should the gift be?

Answer 1

The amount is computed as shown below:

= cost of year 1 / (1 + interest rate)¹ + cost of year 2 / (1 + interest rate)² + cost of year 3 / (1 + interest rate)³ + cost of year 4 / (1 + interest rate)⁴ + cost of year 5 / (1 + interest rate)⁵ + cost of year 6 / (1 + interest rate)⁶ + cost of year 7 / (1 + interest rate)⁷ + cost of year 8 / (1 + interest rate)⁸ + cost of year 9 / (1 + interest rate)⁹ + cost of year 10 / (1 + interest rate)¹⁰ + 1 / (1 + interest rate)¹⁰ x [ (cost after year 10 / interest rate) ]

= 1.4 million / 1.07¹ + 1.4 million / 1.07² + 1.4 million / 1.07³ + 1.4 million / 1.07⁴ + 1.4 million / 1.07⁵ + 1.7 million / 1.07⁶ + 1.7 million / 1.07⁷ + 1.7 million / 1.07⁸ + 1.7 million / 1.07⁹ + 1.7 million / 1.07¹⁰ + 1 / 1.07¹⁰ x [ (1.9 million / 0.07) ]

=  1.4 million / 1.07¹ + 1.4 million / 1.07² + 1.4 million / 1.07³ + 1.4 million / 1.07⁴ + 1.4 million / 1.07⁵ + 1.7 million / 1.07⁶ + 1.7 million / 1.07⁷ + 1.7 million / 1.07⁸ + 1.7 million / 1.07⁹ + 1.7 million / 1.07¹⁰ + 27.14285714 million / 1.07¹⁰

= 1.4 million / 1.07¹ + 1.4 million / 1.07² + 1.4 million / 1.07³ + 1.4 million / 1.07⁴ + 1.4 million / 1.07⁵ + 1.7 million / 1.07⁶ + 1.7 million / 1.07⁷ + 1.7 million / 1.07⁸ + 1.7 million / 1.07⁹ + 28.84285714 million / 1.07¹⁰

= 24.5080816 million or 24,508,081.6