Tonya J.

asked • 02/01/14

The following formula is incorrect for compound interest with the symbols defined this way, can someone tell me why?

The following formula is incorrect for compound interest with the symbols defined this way, can someone tell me why?
 
 
Compound Interest is described by A = P(1+rm)^n, where P is the principal, r is the annual rate, m is the number of compounding periods in 1 year, and A is the amount in the account after n compounding periods.

It is an Exponential function since the exponent is a variable.

4 Answers By Expert Tutors

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Jeff M. answered • 02/01/14

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4.9 (7)

Jeff M, Accounting, Microsoft Excel, Finance, General Business

Tonya J.

This seems right to me but Michael down below there says all answers are wrong but his. Am I missing something?
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02/01/14

Jeff M.

No, Tonya, you're not missing anything.  Michael's answer is correct, but his formula is the same as the formula I was driving at. Using your symbols, the formula should be:
 
A = P * (1 + r/m)^n
 
So, to correct your original formula, the annual interest rate (r) should be divided by the number of compounding periods (m). Your formula multiplied the two, resulting in an overstatement of A. Using the numbers from my example, this makes sense intuitively - the quarterly interest rate is 1.25% (5%/4), rather than 20% (5% * 4).
 
If you plug some numbers into this equation and Michael's, you will get the same result.  I've seen many variations of this formula in practice, which is likely the reason your instructor answered the way (s)he did.
 
Hopefully that makes sense?
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02/02/14

Michael F. answered • 02/01/14

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4.9 (15)

Mathematics Tutor

Tonya J.

Could you explain please?
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02/01/14

Stephen B. answered • 02/01/14

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4.9 (159)

Math Teacher with over 10 Years' Experience

Tonya J.

That's what I thought as well but my instructor felt differently. Here is his response to my formula:
 
"Your formula is incorrect for Compound Interest if you define the symbols the way you did. Look at how the reading defines the symbols."
 
I can't figure out what he means, any ideas?
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02/01/14

Michael F.

tutor
A = P * ((1 + (.05 / 4))^8)
very truly yours
Michael F.
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02/01/14

William S. answered • 02/01/14

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4.4 (10)

Experienced scientist, mathematician and instructor - William

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