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A group of concerned citizens has established a trust fund that pays 5% interest, compounded monthly, to preserve a historical buildingby providing annual maintenance funds of $80,000 forever. Compute the capitalized equivalent amount for these building maintenance expenses.

Answer :

TomShelby

Answer:

The value of the stablish fund is 1,563,663.64 dollars

Explanation:

First, we solve for the effective annual rate as this is a rate which compounds monthly:

[tex](1+APR/m)^m-1 = r_e\\(1+0.05/12)^{12} - 1 = r_e\\r_e = 0.051161898[/tex]

Now, we solve for the Principal of a perpetuity which interest over the year are 80,000:

[tex]\frac{Annuity}{Principal} = rate\\Principal = Annuity \div rate\\Principal = 80,000 \div 0.051161898[/tex]

Principal = 1.563.663,64

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