Money foundations · 14 min

Compounding and the time value of money

Written and reviewed by Prashant Nandkishor Maheshwari (editorial review, 2026-10-18). Not yet checked by an independent subject specialist. How we review.

What you will learn

Calculate how a sum grows with compound interest and explain why time and rate matter so much, for saving and for debt.

Why it matters

Compounding works for you on savings and against you on debts. Seeing the numbers once makes both much easier to judge.

The ideas

Levels are a learning preference, not a credential. Switch any time.

Novice level

Simple interest is paid only on the original amount. Compound interest is paid on the original amount plus the interest already earned, so growth speeds up over time.

The same effect hurts when you owe money. Unpaid interest is added to the balance, and then interest is charged on that bigger balance.

Time matters as much as the rate. Money left to grow for longer gets more rounds of growth.

Basic level

Future value = amount x (1 + rate) ^ years. For monthly compounding use the monthly rate and the number of months.

Rule of 72 (a rough shortcut): years to double is about 72 divided by the yearly rate in percent. At 8% it is about 9 years.

Advanced level

Convert between nominal and effective annual rates: effective = (1 + nominal / m)^m - 1 for m compounding periods a year. Compare offers on the effective rate.

Expert level

Continuous compounding, annuity and perpetuity formulas, and present values of uneven cash flows (net present value, internal rate of return) extend the same idea.

Professional level

Day-count conventions (actual/365, 30/360) and rounding rules change the interest amount in contracts. Use the convention written in the agreement.

Key terms

Compounding: Earning interest on earlier interest.
Future value: What an amount grows to after some time at some rate.
Present value: What a future amount is worth today.
Discounting: Converting a future amount to today's terms.

Worked example

₹1,000 at 8% a year for 10 years. Simple interest: 1,000 + 10 x 80 = 1,800. Compound: 1,000 x 1.08^10 = 2,158.92. The extra 358.92 is interest on interest. Now the other side: a 1,000 unit debt at 24% a year charged 2% each month and left unpaid grows to 1,000 x 1.02^12 = 1,268.24 after a year.

Try it yourself

Use any calculator. Work out what ₹500 a month would become over 5, 10 and 20 years at a yearly rate you choose (try 4% and 8%). Write down what surprises you.

Nothing you write here is collected. Use paper or the workbook.

Try it with numbers: Savings growth calculator.

Check yourself

At 8% a year, roughly how long does money take to double (rule of 72)? About 4 years About 9 years About 18 years

Compounding is only good news. True False

A common misunderstanding

'Starting late does not matter if I save more.' It matters: later money has fewer compounding periods, so catching up needs much larger amounts.

Local context

Quoted rates may be nominal or effective, and compounded monthly, quarterly or yearly. Check how your own product states and compounds its rate.

References and review

Brealey, Myers and Allen, Principles of Corporate Finance (McGraw-Hill), time value of money chapters.
Bodie, Kane and Marcus, Investments (McGraw-Hill).

Author and editorial reviewer: Prashant Nandkishor Maheshwari, 2026-10-18. Independent specialist review is pending. Spotted a mistake? Tell us.

Suggested next step

Continue with 'Mapping your cash flow'.

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