How to quickly calculate compound interest for a period of 54 years?

Question

Hello, PrepLounge Colleagues

I was doing the Casestone Inc case, and it asked the candidate to do the following math:

$100.000 * (1,04)^54 = ?

I do know the rule of 72, so I know the amount will be more than $200.000.

I also know that we can change the compound for simple interest for small tax rates and short periods of time, which is not the case here.

Any suggestions?

Thanks!

Answer 1

Hi Andreia,

this is definitely a case where you can apply the rule of 72 to get a rounded answer:

Step 1: find the amount of time the initial capital would double. Dividing 72 by 4, you get 18
Step 2: find how many times the amount would double in 54 years. As 54/18=3, the amount would double 3 times
Step 3: find the actual value. As $100k would double 3 times, you would get $800k:
- Doubling the first time would go to $200k
- Doubling the second time would go to $400k
- Doubling the third time would go to $800k

The actual answer is $831k thus you would be pretty close.

In this particular case you cannot use shortcuts as the simple interest or the Taylor series, as the period of time is too long.

Hope this helps,

Francesco