What are interest and compounding?
When you deposit money in a bank, the bank lends it to others and pays you something extra in return. That is interest, usually quoted as a percentage per year. When you borrow, it is the reverse: you pay interest. In Islamic banking it is called profit and the contract works differently, but the arithmetic of growth can be understood the same way.
With simple interest, each year’s interest is paid only on the original amount. With compound interest, earlier interest is added to the original, and next year’s interest is paid on that larger sum. In other words, interest on interest.
Say Tania deposits Tk 1,00,000 at 10% a year. With simple interest she earns Tk 10,000 every year; after 20 years she has Tk 3,00,000. With compound interest (never withdrawing the interest) she has about Tk 6,72,700 after 20 years, more than twice the simple-interest total. Tax and inflation are ignored here; the numbers are only an example.
Why it matters to an investor
- Time is the biggest ingredient: compounding is slow at first and fast later. The same money started earlier can end up much larger.
- To compare rates: two offers with similar rates can give different results depending on how often they compound and whether you withdraw the interest.
- To see the true cost of debt: compounding works both ways. Unpaid debt grows the same way savings do.
- To keep expectations realistic: the rule of 72 lets you check in your head whether a promise to “double your money fast” makes sense.
The rule of 72
A quick way to estimate how many years money takes to double: divide 72 by the yearly rate of return. At 9%, 72 ÷ 9 = about 8 years; at 12%, about 6 years. It is an approximation, but very handy for mental arithmetic.
It works in reverse too. If someone promises “double your money in two years”, that needs 72 ÷ 2 = about 36% a year. Returns that high usually come with very large risk, or the promise itself is doubtful.
How often it compounds
Interest can be added once a year, once a quarter or every month. The more often it is added, the slightly higher the true yearly growth. For example, 1% a month compounded works out to about 12.7% a year, not just 12%. This is called the effective annual rate.
- If the interest is paid out monthly or quarterly and you spend it, it no longer compounds; the result is like simple interest.
- How interest is calculated on a deposit or scheme is set out in its terms; don’t judge by the advertised rate alone.
Compounding on debt: the other side
Say an unpaid balance is charged 2.5% a month and you pay nothing off. In a year the balance grows by about 34.5%. A monthly rate that looks small is large over a year. The numbers are only an example.
Worked example
- Tk 1,00,000 at 10% a year. Simple interest: Tk 10,000 every year; Tk 1,30,000 after three years.
- Compound, year 1: Tk 1,00,000 + 10% = Tk 1,10,000.
- Year 2: Tk 1,10,000 + 10% = Tk 1,21,000. Interest is now Tk 11,000, because last year’s Tk 10,000 is earning too.
- Year 3: Tk 1,21,000 + 10% = Tk 1,33,100.
Result: after three years the gap is only Tk 3,100, but after ten years compound gives about Tk 2,59,400 against Tk 2,00,000 simple. Formula: final amount = principal × (1 + rate)^years.
Years
See the numbers as a table
| Compound | Simple | |
|---|---|---|
| 0 | Tk 1 lakh | Tk 1 lakh |
| 1 | Tk 1.1 lakh | Tk 1.1 lakh |
| 2 | Tk 1.2 lakh | Tk 1.2 lakh |
| 3 | Tk 1.3 lakh | Tk 1.3 lakh |
| 4 | Tk 1.5 lakh | Tk 1.4 lakh |
| 5 | Tk 1.6 lakh | Tk 1.5 lakh |
| 6 | Tk 1.8 lakh | Tk 1.6 lakh |
| 7 | Tk 2.0 lakh | Tk 1.7 lakh |
| 8 | Tk 2.1 lakh | Tk 1.8 lakh |
| 9 | Tk 2.4 lakh | Tk 1.9 lakh |
| 10 | Tk 2.6 lakh | Tk 2 lakh |
| 11 | Tk 2.9 lakh | Tk 2.1 lakh |
| 12 | Tk 3.1 lakh | Tk 2.2 lakh |
| 13 | Tk 3.5 lakh | Tk 2.3 lakh |
| 14 | Tk 3.8 lakh | Tk 2.4 lakh |
| 15 | Tk 4.2 lakh | Tk 2.5 lakh |
| 16 | Tk 4.6 lakh | Tk 2.6 lakh |
| 17 | Tk 5.1 lakh | Tk 2.7 lakh |
| 18 | Tk 5.6 lakh | Tk 2.8 lakh |
| 19 | Tk 6.1 lakh | Tk 2.9 lakh |
| 20 | Tk 6.7 lakh | Tk 3 lakh |
Common mistakes
- Giving up because growth looks slow in the early years. Most of compounding’s effect comes towards the end.
- Multiplying a monthly rate by 12 and calling it the yearly cost. With compounding, the true yearly rate is higher.
- Thinking compounding is only about savings. Unpaid loans and card balances balloon the same way.
- Running compounding numbers without taking out tax and inflation. Measure real growth after tax and after inflation.
Compounding needs three things: a rate, time, and leaving the interest in. Time is the most powerful of the three, and on debt it works against you.