A mathematical approach to get anything of monetary value effectively for free using any investment class

The Goal

Interest earned per month should be greater than/equal to the cost of each installment with inflation adjustment. At the end of the purchase, you should have your principal amount adjusted to inflation and the item/service purchased, hence making it effectively free without incurring any monetary loss.

The Math

Factors and variables

1. $A$ = Price of item
2. $m$ = EMI/month
3. $n$ = Number of EMI payments
4. $i$ = Inflation
5. $P$ = Principal amount invested
6. $r$ = Annual interest earned on the principal
7. $d$ = Down payment percentage

Functioning

Effective cost of item after EMI $= A(1+\frac{e}{100})$

$⇒ m = \frac{A}{n}(1+\frac{e}{100})$

$⇒$ Condition: Monthly interest earned $≥ \frac{A}{n}(1+ \frac{e}{100})$

$⇒$ $P(1+\frac{r-i}{100})^{1/12} ≥ \frac{A}{n}(1+\frac{e}{100})$

The Code

Github Repository: KrishGoel/theFreeFormula

theFreeFormula/index.py at main · KrishGoel/theFreeFormula