The Rule of 72 estimates how long it takes for a given amount of money to double
ID: 2792934 • Letter: T
Question
The Rule of 72 estimates how long it takes for a given amount of money to double in value at a fixed compound interest rate. For example, investing $1,000 in a high-yield savings account will earn about 1% interest per year. So, in a few decades (7.2) your money will double. Of course, at 1% per month, the doubling would be in 72 months. (Notice the doubling period is always in the same units of time as the interest rate. Usually, interest is described in annual rates; therefore, the doubling time is in years.) Assume you want to retire at age 60. How much money do you think you will need? What interest rate do you think is a reasonable expectation? By what age will you need to have saved 50% of the final amount? How can you change the time? Explain.
Explanation / Answer
We want to retire by the age of 60. Suppose we need $1 million real value of money at the time of retirement. Currently suppose your are 24 years of age. You have 36 years more before you become 60 years of age. Inflation rate assumed is 2%. This means that in 36 years the value of money will half. (By rule of 72. 72 / 2 = 36 years)
Interest rate of 2% would be a reasonable expectation since it will match the inflation rate and will cancel out the devaluing effect on money because of inflation.
In other word if you invest $1 million at the age of 24 at a interest rate of 2% where inflation is also 2%, then by the age of 60, the amount will be doubled to $2 million. The real value of this amount realized (i.e. $2 million) at the age of 60 is worth $1 million at the age of 24.
Total amount saved in the process is ---> Final Value realized - Initial Value invested i.e. ($2 million - @1 million) = $1 million.
50% of the final amount saved is $0.5 million.
Total amount available at that time is $1 million + $0.5 million = $1.5 million
No of years to realize this value is n (say).
Using the formula: A = P(1 + r/100)^n
where A = $1.5 million, P = $1 million, r = 2% (interest rate), n = no of years.
1.5 = 1 * (1 + 2/100) ^ n
Taking log on both sides
Ln(1.5)/Ln(1.02) = n
n = 20.47 years (In these years you will save 50% of the final amount to be saved).
We can change the time of final amount saved by increasing the interest rate. Suppose you want to decrease the no of years to 18 years, so the interest rate will be 4%.
As per rule of 72, no of years will be 72 / 4 = 18 years.
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