$Question about interest earned$

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$Question about interest earned$

If start out with 300,000peso and earn 10% a month in interest. I roll over all the interest back into the business each month how much will it be worth in .
1 year
2 years
3 years
Thank you for your help this is driving me nuts

Calculus Linear Algebra Precalculus

Roger67

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Suppose you start with $A$ peso (here $A=300,000$) and a monthly interest rate $r$ (here $r=10\%=0.1$). After the 1st month you have $A$ plus the interest $rA$ so you have $$A+rA=(1+r)A $$Now for the 2nd month you started with $B=(1+r)A$ and earn the interest $rB$ so you have $$ B+rB=(1+r)B=(1+r)(1+r)A=(1+r)^2 A$$This way we can see that after $n$ months you have $$(1+r)^nA $$ So after 1 year you get $$ (1+0.1)^{12}\times300,000=941,528$$after 2 years $$ (1+0.1)^{24}\times300,000=2,954,919$$and after 3 years $$ (1+0.1)^{36}\times300,000=9,273,804$$

Martin

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$Question about interest earned$

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