Question

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

Answer 1

Answer:

$2,274,639.75

Explanation:

Endowment on July 2010 = $15,000,000

Endowment amount on July 2014 = $15,000,000 (1+0.05)^4 - Expenditure on facilities

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

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

= $13,232,500

Amount to be set aside for operation expenses = $250,000/0.05 = $5,000,000

Amount available for capital replacement = $13,232,500 - $5,000,000 = $8,232,500

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

Annual available for capital replacements every fifth year forever = $8,232,500 (0.2763) = $2,274,639.75