Question

given the annual interest rate and the compounding period, find i, the interest rate per compounding period:
5% compounded monthly

Answer 1

I do not remember the formula for compounding so I will explain it.

So when you are compounding each month, the principal amount on which you calculate interest is the (principal amount + interest) from previous month

For first month let the Principal Amount be P and interest rate be i. So the interest = P*i/100.
So the principal amount for second month = P + P*i/100 = P(1+i/100)

Answer 2

So for the second month interest = P(1+i/100)*(i/100) so the amount left after adding the interest = P(1+i/100) + P(1+i/100)*(i/100) = P(1+i/100)*(1+i/100)

Answer 3

= P(1+i/100)^2
So for n months we can generalize by saying
the money after n months = P(1+i/100)^n

So after one year (12 months) it is P(1+1/100)^12

Answer 4

Annual Interest Rate = 5%
so if your money if compounded annually and taking the same starting amount (P) after one year you will have
P(1+5/100)

Answer 5

Since in both ways the final amount should be same so,

P*(1+5/100) = P*(1+i/100)^12