Compound interest is interest earned on both the original amount and on the interest already added. Over time, this "interest on interest" makes savings grow faster and faster. It is the reason starting to save early is so powerful — and why debts that compound, such as unpaid credit card balances, can grow so quickly. Understanding compounding is one of the most valuable pieces of financial knowledge anyone can have.
What you will learn
- Calculate compound interest and compare it with simple interest
- Understand the effect of compounding frequency and the effective annual rate
- Use the rule of 72 to estimate doubling time
- Apply compounding to saving, investing and borrowing decisions
Simple versus compound interest
- Simple interest is paid only on the original principal: interest = P × r × t.
- Compound interest is paid on the principal plus accumulated interest.
Compound interest
A = P × (1 + r ÷ m)^(m × t)
where A is the final amount, P the principal, r the annual interest rate, m the number of compounding periods per year and t the number of years. Interest earned = A − P.
Worked example: 100,000 at 9% for 10 years
- Simple interest: 100,000 × (1 + 0.09 × 10) = 190,000.
- Compound interest, annual compounding: 100,000 × 1.0910 = 236,736.
Compounding adds an extra 46,736 — almost half the original principal — with no extra saving. Check figures with the compound interest calculator.
The gap widens dramatically with time:
100,000 at 9%: simple versus compound interest
Show the data
| Years | Compound interest | Simple interest |
|---|---|---|
| 0 | 100,000 | 100,000 |
| 5 | 153,862 | 145,000 |
| 10 | 236,736 | 190,000 |
| 15 | 364,248 | 235,000 |
| 20 | 560,441 | 280,000 |
| 25 | 862,308 | 325,000 |
| 30 | 1,326,768 | 370,000 |
After 30 years, compounding produces more than 3.5 times the result of simple interest.
Compounding frequency
The more often interest is added, the higher the final amount — though the effect is modest compared with the rate and time.
| Compounding | 100,000 at 9% for 10 years |
|---|---|
| Annual | 236,736 |
| Quarterly | 243,519 |
| Monthly | 245,136 |
| Daily | 245,933 |
To compare products with different compounding, use the effective annual rate (EAR):
Effective annual rate
EAR = (1 + r ÷ m)^m − 1
A nominal 12% compounded monthly gives an EAR of (1.01)12 − 1 = 12.68%. Credit cards and loans quoting a monthly rate often have effective annual costs well above the headline figure.
The rule of 72
A quick way to estimate how long money takes to double:
Years to double ≈ 72 ÷ interest rate (%)
At 9%, money doubles in about 72 ÷ 9 = 8 years (the exact figure is 8.04). At 6%, it takes about 12 years; at 12%, about 6 years. The rule works in reverse for inflation: at 6% inflation, prices double in about 12 years, halving the purchasing power of cash — see inflation and real returns.
Time is the most powerful ingredient
Because growth accelerates over time, starting early often matters more than the amount invested. Someone who saves for 25 years instead of 15 can end up with nearly three times as much, even though they contributed only two-thirds more — as shown in the example in introduction to investment. For regular savings, compounding is built into recurring deposits — see FDR and DPS — and into long-term retirement planning.
Compounding works against borrowers too
Unpaid interest on a loan or credit card is added to the balance and then charged interest itself. A balance left unpaid on a card at 30% a year can grow very quickly, which is why paying credit card balances in full is one of the highest-return "investments" available — see credit cards explained.
Real compound growth
What matters for wealth is growth in purchasing power. If savings earn 9% while inflation is 6%, the real growth rate is 1.09 ÷ 1.06 − 1 ≈ 2.8% a year — still compounding, but more slowly. Taxes on interest reduce growth further.
Present value: compounding in reverse
Discounting asks the opposite question: how much is a future amount worth today? It uses the same formula rearranged: P = A ÷ (1 + r)t. This idea underlies loan payments, bond prices and investment appraisal — see time value of money.
Common mistakes
- Comparing interest rates without considering compounding frequency.
- Underestimating how much time adds to growth.
- Withdrawing interest instead of letting it compound.
- Ignoring compounding on debts.
- Forgetting inflation and taxes when projecting growth.
Key terms
- Compound interest — interest earned on principal and on previously earned interest.
- Simple interest — interest earned only on the original principal.
- Compounding frequency — how often interest is added to the balance.
- Effective annual rate — the actual annual rate after allowing for compounding.
- Rule of 72 — a quick estimate of doubling time: 72 ÷ rate.
Frequently asked questions
Is daily compounding much better than monthly?
Only slightly. The interest rate and the length of time have a much larger effect.
Do fixed deposits use compound interest?
Many do, by adding interest to the deposit at intervals or on renewal. Check the terms and whether interest is paid out or reinvested.
How can I benefit most from compounding?
Start early, save regularly, reinvest returns, keep costs low and avoid withdrawing money early.
Key takeaways
- Compound interest earns interest on interest; A = P × (1 + r/m)^(mt).
- Over long periods, compounding far outpaces simple interest.
- Compare products using the effective annual rate; the rule of 72 estimates doubling time.
- Time is the key ingredient — and compounding makes unpaid debts grow quickly too.