# 0% rate of return + inflation differs from inflation alone

Given that

Real Rate of Return = (1 + nominal rate) / (1 + inflation rate) -1

If my nominal rate equals the inflation rate I get 0, meaning that my money is worth the same no matter the inflation rate.

If my nominal rate is greater than the inflation I get positive values, meaning my money is worth more the longer I leave in this investment. And vice-versa.

But something weird happens when the nominal rate is 0%, such as when I leave my money in my wallet. In that case the real rate will be

RR = (1 + 0%)/(1 + 5%) -1 = -4.76%

Am I missing something? How do I interpret that? Shouldn't it be -5%?

EDIT: Also, is there anything wrong with the following formula?

Fake Real Rate of Return = ((1 + inflation rate) / (1 + nominal rate) -1 ) * - 1

In that case when the nominal rate is 0% we get the inflation rate, and when the inflation rate equals the nominal rate we get 0%.

• Percentages aren't additive. 1.05/1.04 - 1 isn't 0.01, either: it's 0.009615.... Jun 3 at 18:04
• Maybe I'm not understading it corretly but the thing is, I'm not changing anything when I put my money on a 'investment' that has no nomial rate, by being very loose about the term investment, the money will devalue by the inflation rate, but when I compute it I get a different result, as if by 'investing it' in a zero nominal rate I changed the real rate of return to be less than the inflation rate. Jun 3 at 18:59
• I think the discrepancy has something to do with the exact Fisher equation vs its approximation.
– Flux
Jun 3 at 20:44