Compound interest
Also written Compounding interest · Power of compounding · Magic of compounding · Compounding
Interest earned on the original amount and also on the interest already earned. Rs 1,000 at 9% grows to Rs 31,409 in 40 years compounded, against Rs 4,600 with simple interest.
In plain language
With simple interest, only your original money earns interest. With compound interest, the interest you earn is added to your money, and from then on that interest earns interest too.
In the first few years the difference is small. Over decades it becomes enormous, which is why the booklet calls it the "magic of compounding" and why it keeps telling readers to start saving and investing early.
How it works
The booklet (Chapter 2) works through Rs 1,000 invested at 9% a year:
| Year | Money at start of year | Return earned | Value at end of year |
|---|---|---|---|
| 1 | 1,000 | 90 | 1,090 |
| 2 | 1,090 | 98 | 1,188 |
| 3 | 1,188 | 107 | 1,295 |
| 10 | 2,172 | 195 | 2,367 |
| 20 | 5,142 | 463 | 5,604 |
| 40 | 28,816 | 2,593 | 31,409 |
The rule it states: principal plus the first year's return becomes the principal for the second year, and so on.
A note on the booklet's table: for year 3 it prints the return earned as 295. The year's return on Rs 1,188 at 9% is about Rs 107; Rs 295 is the total return over all three years (Rs 1,295 − Rs 1,000). The maturity value of Rs 1,295 is right.
With simple interest, the principal stays at Rs 1,000 for all 40 years. At Rs 90 a year, it grows to only Rs 4,600.
The booklet adds the Rule of 72: divide 72 by the annual interest rate to find roughly how many years it takes to double your money. At 6%, 72 ÷ 6 = 12 years.
The formula
Compound interest: Value after n years = P × (1 + r)^n
Simple interest: Value after n years = P × (1 + r × n)
Rule of 72: Years to double ≈ 72 ÷ annual interest rate (in %)
P = amount invested, r = annual rate, n = number of years.
A worked example
The 9% return is illustrative, borrowed from the booklet's own table.
Two friends in Kochi each invest Rs 1,00,000 once and leave it untouched until they turn 60, earning 9% a year compounded.
- Arjun invests at 25. It compounds for 35 years: Rs 1,00,000 × 1.09^35 ≈ Rs 20,41,000.
- Rahul invests at 35. It compounds for 25 years: Rs 1,00,000 × 1.09^25 ≈ Rs 8,62,000.
Same amount, same rate. Ten extra years give Arjun about Rs 11.8 lakh more, more than 11 times what either of them put in.
Check with the Rule of 72: at 9%, money doubles in about 72 ÷ 9 = 8 years. Over 35 years that is a little over four doublings (2^4 = 16, and 1.09^35 ≈ 20.4), which is why Arjun ends near 20 times his money.
Had the same Rs 1,00,000 earned 9% simple interest for 35 years, it would reach only Rs 1,00,000 × (1 + 0.09 × 35) = Rs 4,15,000.
Why NISM asks about it
Chapter 2 (Key Concepts in personal finance) teaches compounding with the Rs 1,000-at-9% table, sets it against simple interest (Rs 31,409 versus Rs 4,600 after 40 years) and gives the Rule of 72. Chapter 5 lists "Power of Compounding – small investments create big kitty over time" as an advantage of a SIP, and Chapter 7 says to start retirement saving early. Expect a Rule-of-72 calculation and a question on which kind of interest earns interest on interest.
Common exam traps
- Simple interest is on the principal only; compound interest is on principal plus earlier interest. Options that swap the two are common.
- Rule of 72 gives years to double, not the rate you need. 72 ÷ 6 = 12 years at 6%.
- The Rule of 72 is approximate. At 9% it says 8 years; 1.09^8 is about 1.99, close to but not exactly 2.
- The booklet's year-3 "return earned" of 295 is cumulative, not that year's return. Rely on the maturity column.
- Time matters more than the starting amount. Starting early is the booklet's repeated advice for exactly this reason.
- Compounding works against you on debt too; the booklet's debt-trap tips warn against treating a credit card as free money.
Check yourself
1.What is the difference between simple interest and compound interest?
- a)Simple interest is paid annually and compound interest is paid monthly
- b)With simple interest you earn interest only on the principal; with compounding you earn interest on the principal as well as on previously earned interest
- c)Simple interest applies to deposits and compound interest applies to loans
- d)Compound interest is always higher in the first year
Show the answer
Answer: (b) With simple interest you earn interest only on the principal; with compounding you earn interest on the principal as well as on previously earned interest
"With SIMPLE INTEREST, you can earn interest ONLY ON THE PRINCIPAL (that is, the amount you initially invested); while with COMPOUNDING interest, you earn interest ON THE PRINCIPAL AS WELL AS, PREVIOUSLY EARNED INTEREST." The mechanism, in the booklet's own note: "Principal + return from the first year collectively becomes the principal for the second year. Principal + return from the second year collectively becomes the Principal for the third year and so on." The consequence is dramatic over long periods: ₹1,000 at 9% grows to ₹31,409 over forty years compounded, while under simple interest "the principal amount remains at ₹1,000 only for all the 40 years and with annual interest of ₹90, the amount grows to ONLY ₹4,600." Option (d) is wrong for a specific reason worth remembering: in the first year the two are identical — the divergence begins only from year two.
Where this is taught
Free preparation for NISM Series SEBI-ICERelated terms
- CAGRThe single smoothed annual rate at which a starting value would have to grow, compounding each year, to reach the ending value over a given period.
- InflationA sustained general rise in the price level, which erodes what a rupee buys — and the reason a nominal return has to be deflated before it means anything.
- Systematic Investment PlanA facility to invest a constant amount into a scheme at regular intervals, which buys more units when the NAV is low and fewer when it is high and so averages the cost of acquisition down.
- Simple interestInterest earned only on the amount you first put in (the principal). The interest is not added back, so it never earns interest of its own, unlike compound interest.
- Time value of moneyThe principle that the same sum of money is worth different amounts at different points on a timeline, because money held today can be invested and because inflation erodes what it will buy.
- Future valueWhat a sum of money invested today will be worth at a future date once returns have been earned and reinvested — the compounding half of the time value of money.
- PMT functionThe spreadsheet function that converts a target corpus into the fixed periodic saving needed to reach it — the arithmetic behind every "how much should I invest a month" answer.
- Market timingTrying to pick the exact best moment to buy or sell. The booklet calls it a "complex or even impossible duty" and offers regular investing (SIP, rupee cost averaging) instead.
- Kisan Vikas PatraA government-guaranteed post office certificate that doubles the amount invested over a fixed term — 124 months in the workbook — with no tax incentive and interest taxed on accrual.
- Defined Contribution (DC) schemeA retirement scheme where the contribution amount is fixed but the eventual pension is not — it depends entirely on the returns earned on the invested corpus.
- Effective yieldThe annual rate that would leave an investor with the same amount after one year as the quoted nominal rate does once its more frequent interest payments are taken into account.