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
The amount that would be available for the capital replacements at the end of every fifth year forever is $2,274,513.93.
Endowment amount:
Endowment amount=[$15,000,000 (1+0.05)^4]- $5,000,000
Endowment amount=[$15,000,000 (1.21550625)] - $5,000,000
Endowment amount= $18,232,594- $5,000,000
Endowment amount= $13,232,594
Capital replacement:
Capital replacement = $13,232,594- ($250,000/0.05)
Capital replacement = $13,232,594 - $5,000,000
Capital replacement = $8,232,594
Effective interest rate :
Effective interest rate = (1+0.05)^5 - 1
Effective interest rate = (1.05)^5 - 1
Effective interest rate = 0.2762815625
Every Fifth year Capital replacements:
Every Fifth year Capital replacements= $8,232,594 ( 0.2762815625)
Every Fifth year Capital replacements=$2,274,513.93
Inconclusion the amount that would be available for the capital replacements at the end of every fifth year forever is $2,274,513.93.
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