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Conditions:

  1. 1 million is the total initial amount I have.
  2. My bank deposits provides me an interest of 4.8% per year after all tax cuts.
  3. Whatever interest amount I receive, I want to be able to get 20% more in the next financial year. For example, if I receive 400 per month in the first year, I would want to receive 480 per month in the next year and 576 per month the year after that.
  4. This should keep on going and should never stop.

I basically want one part of the million to give me a monthly interest, and the other to keep building the principal such that my monthly interest amount keeps increasing by 20% every year. Please help me solve this.

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  • $\begingroup$ You could start by calculating the first two or three years. See if you find a pattern. So this thing of "wanting more interest" - does it mean that the interest rate would grow every year? So that on year $n$, the interest factor is $$ 1.048\times (1.2)^{n-1} $$ $\endgroup$
    – Matti P.
    Nov 19 '19 at 10:50
  • $\begingroup$ Thanks for replying... the interest rate from the bank 4.8% would be constant... With that interest rate, the principal should grow such that my monthly interest amount keeps increasing 20% annually... $\endgroup$
    – Pranav247
    Nov 19 '19 at 10:53
  • $\begingroup$ Try to form an equation for, for example, how much money is on the bank on year $n+1$, as a function of the same number from year $n$. $\endgroup$
    – Matti P.
    Nov 19 '19 at 11:01
  • $\begingroup$ Have you realised that after ten years the monthly interest is about 2477? Do you really wish that? $\endgroup$ Nov 19 '19 at 11:54
  • $\begingroup$ @MichaelHoppe yes I do realize it, but compared to 400 it's quite a lot right... given the rate of inflation, we would still be ahead of the game I guessing... and that was just an example figure... Besides I'm currently more interested in the math behind it... The more I try to calculate, it seems less possible... it's getting very confusing after a point... Please help... $\endgroup$
    – Pranav247
    Nov 19 '19 at 12:21
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If your bank deposits only yield $\ 4.8\%\ $ per year interest, then your goal of deriving an income stream therefrom which increases at a rate of $\ 20\%\ $ per year indefinitely is not achievable. Suppose the income you derive from interest in the first year is $\ \epsilon\ $, and let $\ n\ $ be the smallest positive integer such that $$ \left(\frac{150}{131}\right)^n> \frac{1,000,000}{\epsilon}\ . $$ Then after $\ n\ $ years, your income stream is required to be $\ 1.2^n\epsilon\ $ per annum, but even if all the interest obtained from the bank were devoted to growing the principal, then after $\ n\ $ years the principal would only be $\ 1.048^n\cdot1,000,000\ $, which is less than the income of $\ 1.2^n\epsilon\ $ it is required to generate (because $\ 1.2^n\epsilon = \left(\frac{150}{125}\right)^n\epsilon >$$ \left(\frac{131}{125}\right)^n\cdot1,000,000\ $$=1.048^n\cdot1,000,000\ $).

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