Calculate Interest, Knowing the Annuity, Present Value and Time.

Suppose we decided to pay the $6800 for the time purchase contract in Example 4-4. What monthly rate of return would we obtain on our investment?

SOLUTION

In this situation, we know P, A, and n, but we do not know i. The problem may be solved by using either the uniform seriespresent worth formula


or the uniform series capital recovery formula


Either way,we have one equationwith one unknown.



We know the value of the uniform series present worth factor, but we do not know the interest rate i. As a result, we need to look through several compound interest tables and then compute the rate of return i by interpolation. Entering values from the tables in the appendix, we find


The rate of return,which is between 1/2% and 3/4%, may indeed be computed by a linear interpolation. The interest formulas are not linear, so a linear interpolation will not give an exact solution.

To minimize the error, the interpolation should be computed usinginterest rates as close to the correct answer as possible. [Since a/b = c/d, a = b (c/d)], we write


The mmonthly rate of return on our investmentwould be 0.72% per month.

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