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musickatia
28 days ago
10

A foundation was endowed with $15,000,000 in July 2010. In July 2014, $5,000,000 was expended for facilities, and it was decided

to provide $250,000 at the end of each year forever to cover operating expenses. The first operating expense is in July 2015, and the first replacement expense in July 2014. If all money earns interest at 5% after the time of endowment, what amount would be available for the capital replacements at the end of every fifth year forever
Business
1 answer:
marusya05 [3K]28 days ago
8 0

Answer:

$2,274,639.75

Explanation:

The endowment as of July 2010 was $15,000,000

Endowment value by July 2014 = $15,000,000 (1+0.05)^4 - Facility expenditures

= $15,000,000 (1.2155) - $5,000,000

= $18,232,500 - $5,000,000

= $13,232,500

Funds reserved for operational expenses = $250,000/0.05 = $5,000,000

Available funds for capital replacement = $13,232,500 - $5,000,000 = $8,232,500

Effective interest rate over 5 years = (1+0.05)^5 - 1 = 0.2763

Annual capital replacement funds every fifth year indefinitely = $8,232,500 (0.2763) = $2,274,639.75

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