You have $3000 in an account that yields a nominal return of 6%. If the inflation rate is 3%, how long will you have to leave your money in the account for it to double in real terms?
To find out how long it will take for your money to double in real terms, you need to consider the effect of inflation on the nominal return.
First, let's calculate the real return, which is the nominal return adjusted for inflation. The real return can be calculated using the following formula:
Real Return = (1 + Nominal Return) / (1 + Inflation Rate) - 1
In this case, the nominal return is 6% and the inflation rate is 3%:
Real Return = (1 + 0.06) / (1 + 0.03) - 1
= 1.06 / 1.03 - 1
≈ 0.0291 or 2.91%
Now, let's determine the number of years it takes for your initial amount to double in real terms. To do this, we can use the rule of 72, which states that the doubling time can be estimated by dividing 72 by the annual growth rate:
Doubling Time ≈ 72 / Real Return
In this case, the real return is 2.91%:
Doubling Time ≈ 72 / 2.91
≈ 24.7
Therefore, it would take approximately 24.7 years for your money to double in real terms.