# calculating the total amount compunded anually

I invest 10000$every month for 15 year I want to know how much money I will get after 15 years if I have 10% interest compounded annually.Any formula to find this.Whats the amount i will receive at the end of 15th year including interest? - ## 2 Answers It looks like you're investing some amount$T$annually, and compounding once at the end of the year with an interest rate$r$. You'd like to find the value$v_n$after the n$^\text{th}$year, given that$v_{n+1} = (v_n + T)(1+r)$, and that$v_1 = T(1+r)$(as there's no initial 0$^\text{th}$month investment). This guy's not so hard to solve by looking for patterns: $$v_{n+1} = v_1 (1+r)^n + T \sum_{k=1}^n (1+r)^k = T \frac{1+r}{r}\left((1+r)^{n+1}-1\right) ~~.$$ The amount invested annually is$12\times\$10000$, the annual rate is $0.1$, and the number of years (above $n+1$) is $15$, so the value of the investment will be ...

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This link contains a lot about compound interest starting with basics.. http://www.math.hawaii.edu/~ramsey/CompoundInterest.html

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