# Case: Quick Way to Calculate Compounded Interest

Case Case Calculations Cases Compounded Annual Growth Rate Math problem
Recent activity on Jan 09, 2017
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Hi everyone!

I know the formula for the investment with compounded interest (V=P[1+(r/n)^n*t]), but do you know of good ways to quickly calculate it in your head?

Like for example when you have an annual growth of 5% for 10, 50 or 70 years or so, how could you quickly estimate it during the case interview?

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

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

Thank you, Francesco!!! It's funny how I already knew the method all along! Thank you so much for your help!

Ever heard of the rule of 70?
For relatively low percentages (<10%) you can approximate the time to double an amount by dividing 70 by the percentage number.

So at 2% interest, your money will (roughly) double in 35 years, at 3% it would take you about 23 years.

This will of course not anwer every question, but it may give you some helpful guidance.

Dear Anonymous C,

thank you for asking your question on our Forum and taking part in the discussion :)

If you have further questions on quick NPV calculations, feel free to open a new thread on our Forum!

Astrid

PrepLounge Community Management Could anybody also give a hint how to calculate a NPV in your head? Would be great

You can say that you understand that to get the exact answer one must deal with compound percentages and that you know exactly how to do that. However, for the purposes of this case and in view of the time limitations you will assume 5% per year over 10 years is simply 50% increase at the end of the 10 year period, which would be an underestimation. Then you must ask the interviewer if they are fine with it.