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

 

[asiacup2025]

Hi David,

It looks like the issue is with the exponent you’re using. For compound interest, the formula is A = P(1 + r/n)^(n×t). Since the interest is compounded semiannually, n = 2, and for 7 years, the exponent should be 2 × 7 = 14, not 9. That’s why your result is too low.

Also, when checking your numbers or rounding intermediate steps, a tool like a Rounding Calculator can be really useful to make sure your calculations are accurate before multiplying by the principal. It helps avoid small errors that can grow in compound interest problems.

 

[Dr.Peterson]

Hi David,

David hasn't been on the site in almost 7 years. Why are you bothering to answer?

It looks like the issue is with the exponent you’re using. For compound interest, the formula is A = P(1 + r/n)^(n×t). Since the interest is compounded semiannually, n = 2, and for 7 years, the exponent should be 2 × 7 = 14, not 9. That’s why your result is too low.

The question was already answered; he knows (if he remembers after all this time) that his mistake was to add rather than multiply:

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.

What someone should have pointed out is that he was thinking the formula calls for multiplying two powers (a^m * a^n), when in fact it calls for using the product of two numbers as a single exponent: A = P (1 + r/n)^(nt). Hopefully he realized that a^(nt) is not the same as a^n a^t = a^(n+t).

Also, when checking your numbers or rounding intermediate steps, a tool like a Rounding Calculator can be really useful to make sure your calculations are accurate before multiplying by the principal. It helps avoid small errors that can grow in compound interest problems.

Are you just advertising that site? It's utterly irrelevant to this problem; actually, you should never round intermediate steps! You should round only at the end (to the nearest cent, presumably).

The site also neglects the most important thing: how to decide which rounding method is appropriate to a particular problem. Why describe ten methods (though you only support five) without explaining that?