Cookie and Privacy Settings

This website uses cookies to enable essential functions like the user login and sessions. We also use cookies and third-party tools to improve your surfing experience on preplounge.com. You can choose to activate only essential cookies or all cookies. You can always change your preference in the cookie and privacy settings. This link can also be found in the footer of the site. If you need more information, please visit our privacy policy.

Data processing in the USA: By clicking on "I accept", you also consent, in accordance with article 49 paragraph 1 sentence 1 lit. GDPR, to your data being processed in the USA (by Google LLC, Facebook Inc., LinkedIn Inc., Stripe, Paypal).

Manage settings individually I accept
expert
Expert with best answer

Francesco

100% Recommendation Rate

3,031 Meetings

7,642 Q&A Upvotes

USD 429 / Coaching

5

Case: Quick Way to Calculate Compounded Interest

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?

Thanks in advance for your help!

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?

Thanks in advance for your help!

(edited)

5 answers

  • Upvotes
  • Date ascending
  • Date descending
Best Answer
Book a coaching with Francesco

100% Recommendation Rate

3,031 Meetings

7,642 Q&A Upvotes

USD 429 / Coaching

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

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! — Andreia on Mar 04, 2018

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.

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 :)

Have you already seen the Forum thread on NPV calculations?
I think the answers might be helpful for you.

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

Good luck for your preparation,

Astrid

PrepLounge Community Management

PrepLounge Consulting Q&A Forum

Follow us on: Facebook | Instagram | LinkedIn | twitter

Dear Anonymous C,

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

Have you already seen the Forum thread on NPV calculations?
I think the answers might be helpful for you.

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

Good luck for your preparation,

Astrid

PrepLounge Community Management

PrepLounge Consulting Q&A Forum

Follow us on: Facebook | Instagram | LinkedIn | twitter

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

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.

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.

Related BootCamp article(s)

CAGR - Compound Annual Growth Rate

Learn everything you need to know about CAGR (Compound Annual Growth Rate) for your case interview ✔ Definition ✔ Formula ✔ Examples ✔ Applications

Typical Question Types in Written Tests

Questions among all tests can be categorized in math, GMAT-style, chart reading and brain teaser questions. Each type needs to be approached differently.

Guide to Improving Speed in Written Tests such as the PST

Follow these instructions to significantly improve your performance and speed in solving problem solving tests used at McKinsey, BCG and Bain.

Which companies are currently using written tests ?

All major firms like McKinsey, BCG and Bain use tests to assess a candidate's analytical skills. However the design of those tests can differ a lot.

Related case(s)

REA Reinsurance

Solved 11.2k times
REA Reinsurance Your client, REA, is a reinsurance company. REA recently acquired another reinsurance company (approximatively same size): the choice of this company was notably based on its product portfolio as well as its market presence which appeared complement with REA. However, the acquisition is not well received by the market. The acquisition price is considered too high and the transaction has not been well graded. REA management asks you to evaluate the transaction.
4.1 5 948
| Rating: (4.1 / 5.0)

Your client, REA, is a reinsurance company. REA recently acquired another reinsurance company (approximatively same size): the choice of this company was notably based on its product portfolio as well as its market presence which appeared complement with REA. However, the acquisition is not well r ... Open whole case

MBB Final Round Case - Smart Education

Solved 9.1k times
MBB Final Round Case - Smart Education Our client is SmartBridge, a nonprofit educational institution offering face-to-face tutoring services. The client operates in the US. The mission of SmartBridge is to help as many students as possible to complete studies and prevent that they drop from the school system, in particular in disadvantaged areas. The client is considering starting operations for its services in the Chicago area. They hired us to understand if that makes sense. Due to the nonprofit regulation, SmartBridge should operate on its own in the market, without any partnership. How would you help our client?
4.6 5 370
| Rating: (4.6 / 5.0)

Our client is SmartBridge, a nonprofit educational institution offering face-to-face tutoring services. The client operates in the US. The mission of SmartBridge is to help as many students as possible to complete studies and prevent that they drop from the school system, in particular in disadvant ... Open whole case

Hospital's ill finances

Solved 6.8k times
Hospital's ill finances A firm managing hospitals has recently been experiencing growing pains. It has contacted our firm to ask for help.
4.4 5 765
| Rating: (4.4 / 5.0)

A firm managing hospitals has recently been experiencing growing pains. It has contacted our firm to ask for help. Open whole case

Espresso, Whatelse?

Solved 6.6k times
Espresso, Whatelse? Espresso Whatelse is an Italian company that produces coffee and espresso machines since 1908. It is the Italian market leader and has a strong presence overall in Europe. In 2019, Espresso Whatelse has increased its revenues but it has seen declining profit margin. Your client wants to understand the root causes of this 2019 trend and how to increase its profit margin again.  
4.6 5 337
| Rating: (4.6 / 5.0)

Espresso Whatelse is an Italian company that produces coffee and espresso machines since 1908. It is the Italian market leader and has a strong presence overall in Europe. In 2019, Espresso Whatelse has increased its revenues but it has seen declining profit margin. Your client wants to understand ... Open whole case

AirService

Solved 5.5k times
AirService Your client AirService is the service provider for a number of airports. The management realized a decrease in profits that is linked to increasing costs. How would you help them?
3.9 5 835
| Rating: (3.9 / 5.0)

Your client AirService is the service provider for a number of airports. The management realized a decrease in profits that is linked to increasing costs. How would you help them? Open whole case