Compounding
Growth on growth: how time, rate and frequency change the answer, and why the assumed rate matters most
Inflation and yield figures as on the dates shown
Verified 12 October 2026
For training and education only. Not investment advice.
Trainer notes
Ask the room: ₹1 lakh grows at 8% a year. After 30 years, is it nearer ₹3.4 lakh or ₹10 lakh? Then ask what would have to be true for either answer to hold. Keep both answers for slides 4 and 5.
Compounding means growth is added to the base, so the next period's growth is worked out on a larger base.
It is arithmetic, not a feature of any product. It needs a rate. For anything market-linked, that rate is not fixed, is not known in advance and can be negative.
Trainer notes
Every rate in this deck is an assumption chosen to make the arithmetic clear, except the three dated figures on slide 10. Do not let any assumed rate be heard as what an investor can expect. Returns are not assured.
Three inputs, one formula
Principal
The amount at the start. Under compounding, each period's growth is added to it and becomes part of the base.
Rate
The growth in one period, as a percentage of the base. In a formula it is fixed. In a market-linked investment it is not.
Periods
How many times growth is added. More years, or growth added more often within a year, both mean more periods.
Take-away: Amount = principal × (1 + rate per period) raised to the number of periods.
Trainer notes
Write the formula on the board with numbers: ₹1,00,000 × 1.08 × 1.08 × 1.08. 'Raised to the number of periods' only means multiplying by (1 + rate) that many times. Simple growth, by contrast, is principal × (1 + rate × number of periods).
Simple and compound, side by side
THREE YEARS AT 8%
₹1,00,000 is left untouched for three years.
Assumed rate: 8% a year.
First as simple growth, then compounded once a year.
- Simple: 8% of ₹1,00,000 is ₹8,000 a year. After three years: ₹1,00,000 + 3 × ₹8,000 = ₹1,24,000.
- Compound, year 1: ₹1,00,000 × 1.08 = ₹1,08,000. Year 2: ₹1,08,000 × 1.08 = ₹1,16,640.
- Compound, year 3: ₹1,16,640 × 1.08 = ₹1,25,971.20.
- The difference is ₹1,971.20. All of it is growth worked out on earlier growth.
Result: Simple growth adds the same amount each year. Compound growth adds a larger amount each year.
Illustration. The 8% rate is an assumption for the arithmetic, not a forecast.
Trainer notes
Answer to the opening question: at an assumed 8% for 30 years, simple growth gives ₹3,40,000 and yearly compounding gives ₹10,06,266. Both answers were right for one method. The gap is small after three years and large after thirty, which is the subject of the next slide.
What time and rate do
| Assumed 4% a year | Assumed 8% a year | Assumed 12% a year | |
|---|---|---|---|
| 0 | 1 | 1 | 1 |
| 5 | 1 | 1 | 2 |
| 10 | 1 | 2 | 3 |
| 15 | 2 | 3 | 5 |
| 20 | 2 | 5 | 10 |
| 25 | 3 | 7 | 17 |
| 30 | 3 | 10 | 30 |
Read the chart
- Each line starts at ₹1 lakh and is compounded once a year. Only the assumed rate differs.
- Time: at 8%, the first ten years add ₹1.16 lakh. The last ten add ₹5.40 lakh.
- Rate: after 30 years the lines reach ₹3.24 lakh, ₹10.06 lakh and ₹29.96 lakh.
- The lines are smooth only because each rate is fixed by assumption.
Illustrative data: ₹1,00,000 × (1 + rate) raised to the number of years. The three rates are assumptions, not forecasts.
Trainer notes
Two points to draw out. First, most of the growth comes late, so the number of periods matters a great deal. Second, doubling the rate much more than doubles the result over long periods. Then the caution: a market-linked value does not follow a smooth line, and none of these rates is what any investment can be expected to earn.
How often growth is added
₹1,00,000 for one year at an assumed 12% a year, with growth added at different intervals.
| Growth added | Working | After one year | Effective yearly rate |
|---|---|---|---|
| Once a year | ₹1,00,000 × 1.12 | ₹1,12,000.00 | 12.00% |
| Every six months | ₹1,00,000 × 1.06 × 1.06 | ₹1,12,360.00 | 12.36% |
| Every quarter | ₹1,00,000 × 1.03, four times | ₹1,12,550.88 | 12.55% |
| Every month | ₹1,00,000 × 1.01, twelve times | ₹1,12,682.50 | 12.68% |
Illustration. The 12% rate is an assumption for the arithmetic. Amounts are rounded to the nearest paisa.
Trainer notes
The same quoted rate gives different results depending on how often growth is added, so always ask how a rate is compounded. This is why '1% a month' is not the same as '12% a year': 1% a month compounds to 12.68% a year. The effect of frequency is real but small next to the effect of time and of the rate itself.
The Rule of 72: how close is it?
A shortcut: years to double ≈ 72 ÷ the yearly rate in per cent. It is an approximation.
| Assumed yearly rate | 72 ÷ rate | Exact years to double | The shortcut is |
|---|---|---|---|
| 4% | 18.0 years | 17.67 years | 0.33 year too long |
| 6% | 12.0 years | 11.90 years | 0.10 year too long |
| 8% | 9.0 years | 9.01 years | 0.01 year too short |
| 12% | 6.0 years | 6.12 years | 0.12 year too short |
| 24% | 3.0 years | 3.22 years | 0.22 year too short |
Exact figures are for growth compounded once a year: log 2 ÷ log (1 + rate). All rates are assumptions for the arithmetic.
Trainer notes
The rule is closest near 8% and drifts as the rate moves away from it. It only tells you how long doubling takes if the rate holds every year, which no market-linked investment does. It works for anything that compounds, including prices: at an assumed 6% inflation, prices double in about 12 years.
It works on costs and prices too
Prices
At an assumed 5% a year, something that costs ₹100 today costs ₹265.33 in 20 years. Inflation compounds.
Costs
₹1 lakh for 20 years at an assumed 10% a year becomes ₹6.73 lakh. If costs take 1 percentage point a year, 9% gives ₹5.60 lakh.
Losses
A fall of 50% needs a gain of 100% to get back to the start. A fall of 20% and then a gain of 20% leaves ₹96 of every ₹100.
Take-away: Compounding has no direction of its own. It multiplies whatever rate it is given.
Trainer notes
Working: 1.05 raised to 20 = 2.6533. 1.10 raised to 20 = 6.7275 and 1.09 raised to 20 = 5.6044; the difference, ₹1.12 lakh, is 16.7% of the larger figure. 0.80 × 1.20 = 0.96. All rates are assumptions. The cost example is arithmetic on two assumed rates; it is not a comparison of any two schemes or plans.
A projection is only as good as its rate
₹10,000 paid at the end of each month for 20 years: 240 instalments, ₹24,00,000 paid in.
| Assumed rate a month | Same as, a year | Result at rate | Growth or loss |
|---|---|---|---|
| −0.25% | −2.96% | ₹18,06,402 | Loss of ₹5,93,598 |
| 0% | 0% | ₹24,00,000 | Nil |
| 0.25% | 3.04% | ₹32,83,020 | Growth of ₹8,83,020 |
| 0.50% | 6.17% | ₹46,20,409 | Growth of ₹22,20,409 |
| 0.75% | 9.38% | ₹66,78,869 | Growth of ₹42,78,869 |
Illustration. Each rate is an assumption, compounded monthly; none is a forecast. Actual returns vary from month to month.
Trainer notes
The instalments and the 20 years are the same in every row; only the assumed rate changes, and the answer runs from ₹18 lakh to ₹67 lakh. A calculator gives one row of this table. When anyone shows a projected value, ask which rate was assumed, how it is compounded, and whether costs, tax and inflation are counted. Never present a row as what a client will get.
Three rates that are not assumptions
Measured or official figures, with dates. Each is a reading for its date, not a rate to project forward.
- CPI INFLATION
- 4.82%Rise in consumer prices over the year to August 2026. Provisional.
- INFLATION TARGET
- 4%Set by the Government for 1 April 2026 to 31 March 2031, with a band of 2% to 6%.
- 10-YEAR G-SEC YIELD
- 6.96%Yield on the 6.94% Government security maturing in 2036, on 1 September 2026: 6.9570%.
Sources: MoSPI CPI press release, 14 Sep 2026 (base 2024=100); Government notification of the inflation target, Mar 2026; RBI Current Rates, 1 Sep 2026.
Trainer notes
Use these to show what a real rate looks like: it has a date, a source and a definition, and it changes. Inflation was 4.82% for one twelve-month period; nobody knows the figure for the next twenty years. A bond yield moves every day. As arithmetic only: prices rising at exactly 4% a year would double in about 17.7 years. Market figures are shown with a lag of at least 30 days, in line with SEBI's norms on price data used for education.
Four things people get wrong
Misconception'Double the rate, double the result.'
What is trueOver 30 years, ₹1 lakh at an assumed 4% becomes ₹3.24 lakh. At 8% it becomes ₹10.06 lakh: more than three times as much.
Misconception'The Rule of 72 is exact.'
What is trueIt is a shortcut. At 24% it says 3.0 years; the exact figure is 3.22 years.
Misconception'Compounding always works for me.'
What is trueIt also works on costs, on rising prices and on losses. It multiplies whatever rate it is given.
Misconception'The calculator shows what I will get.'
What is trueIt shows what an assumed rate produces. No market-linked investment has a fixed rate. Returns are not assured.
Trainer notes
The fourth point is the one that matters in front of a client. A projected value is the output of an assumption, and the assumption is the weakest part. We do not tell a client what rate to expect.
Check yourself
Question 1: ₹50,000 grows at an assumed 10% a year for two years. What is it worth with simple growth, and with growth compounded once a year?
Answer: Simple: ₹50,000 + 2 × ₹5,000 = ₹60,000. Compound: ₹50,000 × 1.10 × 1.10 = ₹60,500. The extra ₹500 is 10% of the first year's ₹5,000.Question 2: Using the Rule of 72, about how long does an amount take to double at an assumed 9% a year? Is the answer exact?
Answer: 72 ÷ 9 = 8 years. It is an approximation: the exact figure with yearly compounding is about 8.04 years, and only if the rate holds every year.Question 3: A client shows a calculator result: '₹10,000 a month becomes ₹67 lakh in 20 years.' What do you ask and explain?
Answer: Ask which rate was assumed and how it is compounded (here 0.75% a month). Explain that the figure is the output of that assumption, that at 0.25% a month the same instalments give about ₹33 lakh and at a negative rate less than was paid in, that costs, tax and inflation are not counted, and that returns are not assured. Do not suggest which rate is likely.
Trainer notes
Quiz figures are invented for the arithmetic.
Sources and disclaimer
Sources for the figures in this explainer
- CPI inflation 4.82% for August 2026 (provisional, base 2024=100): Ministry of Statistics and Programme Implementation, press release of 14 Sep 2026.
- Inflation target of 4% with a band of 2% to 6% for 1 Apr 2026 to 31 Mar 2031: Government of India notification under the Reserve Bank of India Act.
- 10-year Government security (6.94% GS 2036) yield 6.9570% on 1 Sep 2026: Reserve Bank of India, Current Rates (page archived 2 Sep 2026).
- Every other rate, amount and result in this deck is an assumption or is computed from one, for illustration. None is a forecast or an expected return.
This material is for training and investor education only. It is not investment, tax or legal advice and is not a recommendation to buy, sell or hold any security or scheme. Examples use assumed figures unless a source and date are shown. Mutual fund investments are subject to market risks; read all scheme related documents carefully. Trustner Asset Services Pvt. Ltd. is an AMFI-registered Mutual Fund Distributor (ARN-286886).