Calculator giving wrong answer to compound interest problem.

[davidneedsmathhelp]

I am using this formula to calculate compound interest.

A = P (1 + r/n)^(nt)

Find the accumulated value of an investment of $10,000 for 7 years at an interest rate of 4.5% compounding semiannually.

When I divide 0.045 by 2, add 1, raise the result to the 9th power, and finally multiply 10000 by that result, I am getting 12,217.15, rounding to the nearest cent. The answer should be 13,654.83

Can someone tell me what I am doing wrong? Thanks!

 

[JeffM]

Why are you dividing 0.045 by 2? Does the problem specify semi-annual compounding? (If so, you need to say so explicitly. We ask that you give problems exactly and completely.)

Assuming that we are dealing with semi-annual compounding, in which case dividing by 2 is correct, why are you raising to the NINTH power? How many semi-annual periods are there in seven years?

 

[davidneedsmathhelp]

Why are you dividing 0.045 by 2? Does the problem specify semi-annual compounding? (If so, you need to say so explicitly. We ask that you give problems exactly and completely.)

Assuming that we are dealing with semi-annual compounding, in which case dividing by 2 is correct, why are you raising to the NINTH power? How many semi-annual periods are there in seven years?

Hi Jeff. I am raising to the 9th power because t = 7, and n = 2 (semiannual). I believe the exponent product rule is a^m * a^n =a^m+n

When I multiply the exponent 7 and 2 instead of adding them, I am getting the correct answer. Silly mistake by me, I appreciate the help.

 

[tkhunny]

7 * 2 = 14