Challenge Problem: Feb 2005: monthly compound interest

[imtrying]

It's pretty late after work now. So maybe I'm really confused. I'm staring at it but nobody seems to have raised questions about this problem.

The first sentence of the problem says: A certain sum was invested in a high-interest bond for which the interest is compounded monthly.

statement 1 says: The interest rate during the period of investment was greater than 39 percent but less than 45 percent.

And the explanation starts with this formula: FV = PV x ( 1 + r/100) ^ n

Without giving away any further part of the problem, this solution is wrong already. For an annual interest r, if you compound it monthly, the formula should be FV = PV x ( 1 + r/1200) ^ n. At the start, the solution fails to divide the annual interest rate by 12 months before it is compounded. Therefore I think the official answer is incorrect.

Since nobody asked about this before, am I missing something obvious?

[Caveman]

The original formula is correct, since it is a general form.

The term r in this case will be r/12, where r is the yearly rate of interest.

The term n (number of compounding terms) gets multiplied.

Hence for your case, n will be 12 * number of years.

If the interest is compounded quarterly, then r become r/4 and and n is 4 x n

[imtrying]

Thanks.

I agree with the formula. However, if you put it in the context of the problem and the official solution, it was not applied correctly. This is the 'Feb 2005 Taking an interest' problem. The solution basically applies the annual interest 'r' and compounds it monthly, rather than the monthly interest 'r/12' and compounds it monthly. Therefore, the numbers at the end of the solution were incorrect.

[esledge]

I'm going to forward this to our curriculum director for review.

The OG seems to consistently specify "the annual interest rate" rather than just talking about "the rate." Rate is meaningless without a time frame: Would you rather make 10% in a single year or over 50 years?

Nice catch--thanks!