A building owner has $10,000 available and has the option to invest this money in either (i) a bank that has an annual interest rate of 7 percent or (ii) buying a new boiler for the building. If he decides to invest all the money in the bank, how much will the building owner have after ten years? Compare

Question

A building owner has $10,000 available and has the option to invest this money in either (i) a bank that has an annual interest rate of 7 percent or (ii) buying a new boiler for the building. If he decides to invest all the money in the bank, how much will the building owner have after ten years? Compare this amount if simple interest had been paid.

Accepted Answer

If the interest is compounded, using Eq. (3.6) with P = $10,000, N = 10, and i = 0.07, the investment will accumulate to the total amount F:

[latex]F = F_{N + 1} = (1 + i)^{N} P[/latex] (3.6)

F = $10,000 * [latex](1+ 0.07)^{10}[/latex] = $19,672

Thus, the building owner’s original investment will have almost doubled over the ten-year period.

If simple interest had been paid, the total amount that would have accumulated is slightly less and is determined from Eq. (3.3):

F = P + I = P(1+ Ni) (3.3)

F = $10,000 * (1+ 0.07 *10) = $17,000

Question 3.1: A building owner has $10,000 available and has the option to...

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