Help with math problem

Question

When you rewrite the compound interest formula to find a different rate that will keep A and P the same when n changes, you multiply the exponent by 1 since multiplying by 1 doesn't change a number's value. Suppose n changes from 1 to 12 to represent a change from compounded annually to compounded monthly. What is the benefit of using 1=1/12⋅12?

The 12 in the exponent shows that when the interest is compounded monthly, since it is compounded

12 times per year.

There is no particular benefit to this. You can use any 1, such as 1=14⋅4 and still keep A and P the same while compounding monthly.

It is beneficial, because if you use any 1 other than 1=112⋅12, A and P will change.

This is not beneficial. Compounding frequency is represented by t not n, so any 1 you multiply n by would work.

Answer 1

I am not sure of the exact notations you are using. You seem to have asked a few questions here. It seems you use n for compounding frequency and t for year. That can make things a little confusing. If interest is compounded annually at some rate ,i, the effective equivalent monthly compounding rate will be (1+I)^1/12 -1 which is less than i/12.