Risk free rate formula breakdown

Question

In risk free rate formula below why is 1 added on numerator and denominator and the value is substracted by 1

Rf = (1+nominal risk free rate)/(1+inflation) -1

Answer 1

Most simply because math. It's been too long since my formal education on these topics so I don't remember the actual mathematic terms for this but essentially adding the 1 to an interest rate simply includes the principle in your solution, removing the 1 removes the principle. As an example, to calculate a 7% tax on $50, you can do 50 * 0.07 = $3.50, to calculate the total including tax you would do 50 * 1.07 = $53.50.

If an interest rate is 10% = 0.1; and inflation is 3% = 0.03.

0.1 / 0.03 = 3.333333

1.1 / 1.03 = 1.0679

In one case you come up with 333% in one case you come up with 106%. You subtract 1 to remove what would be the principle so you're back to focusing on only the rates, so the risk free interest rate is 6.7%.