A municipal contractor has agreed to construct an electric power plant and to de

Question

A municipal contractor has agreed to construct an electric power plant and to deposit sufficient money in a perpetual trust fund to pay a $10,000/year operating cost and to perform a major renovation to the plant every 15 years at a cost of $200,000. The first renovation is to take place fifteen years from now. The plant itself will initially cost $500,000 to construct. If the trust fund earns 10% interest per year (compounded annually), what is his capitalized cost to construct the plant, to make the future periodic renovations, and to pay the annual operating costs forever.

Explanation / Answer

OPERATING COST
We need $10000 annualy.
The amount to be set aside :
10000/i
= 10000/10%
= $100,000

RENOVATION COST

In every 15 years we need to accumulate $200,000. This should be done via interests.
Let the amount be 'X'.
X*[(1+i)^15 - 1] = 200,000
X = $62,947 ~ $63000

INITITAL COST
This is $500,000

THUS, TOTAL COST = 100000+63000 + 500000 = $663,000

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