# How much would 1 million make me per month in interest with the conditions mentioned in the description?

## 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.

• 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 $$1.048\times (1.2)^{n-1}$$ Nov 19 '19 at 10:50
• 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... Nov 19 '19 at 10:53
• 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 $n$. Nov 19 '19 at 11:01
• Have you realised that after ten years the monthly interest is about 2477? Do you really wish that? Nov 19 '19 at 11:54
• @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... Nov 19 '19 at 12:21

## 1 Answer

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\$$).