# What is the formula for compound interest? Amount=Principal*(1+(r/100))^n But please simplify it taking compoundinterest as the subject For eg-ci=.. Please give a step-by-step explaination on...

What is the formula for compound interest?

Amount=Principal*(1+(r/100))^n But please simplify it taking compoundinterest as the subject For eg-ci=..

Please give a step-by-step explaination on this question.

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### 1 Answer

The formula A=P(1+r/100)^n gives the amount of money in an account given an initial investment of P dollars, invested at an interest rate of r% for a period of n years, compounded yearly.

Year 0 you invest P dollars.

After 1 year you earn P*r/100 dollars in interest, and now have P+P*r/100 or P(1+r/100) dollars. ** Factor out the common P

After year 2 you earn interest on your total account:

P(1+r/100)(1+r/100)=P(1+r/100)^2

**This is [P(1+r/100)]+[P(1+r/100)(1+r/100)]. The first term is the amount of money in your account at the end of the year before interest, and the second term is the amount of interest earned that year. Factor out the common P(1+r/100) to get the result.

After year three:

P(1+r/100)(1+r/100)(1+r/100)=P(1+r/100)^3

etc...