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Basic Math/Average & Compound Interest

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Expert: Josh - 4/9/2009


Question
Hello:

How is the average determined for the following amount if it earns compound interest?

Here are my calculations, but I'm not certain that they are correct: Initial amount invested $500.00:

$500.00 @ 5% = $525.00.

$525.00 @ -2% = $514.50.

$14.50/$500.00 = 2.9% divided by 2 equals an average of 1.45%.  

If this average, 1.45%, is correct, how can I use 5% and -2% to determine the same average?
Is it possible?

I thank you for your reply.

Answer
Hi Kenneth,

Let r=0.05, s=-0.02 and P=500.

The overall change is given by P*(1+r)*(1+s)-P.
What you have done is divide this by P to obtain the relative change.
You further divide this by 2 to obtain the average.
Then, multiply it by 100 to get a percentage.

This is equivalent to doing [P*(1+r)*(1+s)-P]/(2P) *100

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Josh

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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.

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I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.

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Bachelor degree in Engineering Science

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