# Investing

## Compound interest is the same for Roth and Traditional IRAs

It is a common misconception that because of compound interest a Roth IRA will have a different return than a Traditional IRA. Modeling the return for an IRA mathematically will make it obvious that there is no difference.

With:

- p = principal
- r = interest rate
- t = tax rate
- y = years

Return = (1-t)p(1+r)^{y}

Because of the associative property of multiplication, it does not matter if the tax is applied before (Roth) or after (Traditional), since all the elements are multiplied.

((1-t)p)(1+r)^{y} = (1-t)(p(1+r)^{y})