Back-of-the-Envelope Estimates

You don’t always need a calculator or spreadsheet. Back-of-the-envelope estimates use rounding and simple reasoning to get answers that are roughly right, which is often enough to make a good decision.

Fermi estimates

Physicist Enrico Fermi was famous for estimating things quickly with little data, such as how many piano tuners work in a city. The approach:

1. Break the question into smaller parts.
2. Make reasonable guesses for each.
3. Multiply or add them.

Money examples

How much does a daily coffee cost a year? 50 rupees x 365 days = about 18,000 rupees.

How much could that become if invested for 20 years at 10 percent? Saving about 1,500 rupees a month for 20 years at 10 percent grows to roughly 11 lakh rupees.

Can I afford this car? A 10 lakh car loan at 9 percent over 5 years has an EMI of roughly 20,000 rupees. Is that under 15 to 20 percent of your take-home pay?

Handy shortcuts

• Rule of 72: years to double = 72 / interest rate.
• 1 percent of a crore = 1 lakh.
• Per day to per year: multiply by 365 (or roughly 350 for easy maths).
• Monthly to yearly: multiply by 12.
• EMI rule of thumb: a 1 lakh loan at around 9 to 10 percent costs roughly 2,100 rupees a month over 5 years and about 900 rupees a month over 20 years.

Module recap

• EMIs combine interest and principal, and longer tenures cost much more.
• Flat rates are far costlier than they appear; compare APRs.
• CAGR shows real growth; XIRR handles regular investments.
• Present value compares lump sums with payment streams.
• Break-even, unit prices and discount maths guide business and shopping.
• Prepaying by cutting tenure saves most interest.
• Withdrawal rates of about 3 to 4 percent guide retirement planning.