What compound interest is
Simple interest is paid only on the amount you put in at the start (the principal). Compound interest is paid on the principal and on the interest already added to it. Each time interest is credited, the base for the next calculation grows, so the next interest amount is larger than the last.
This effect is often called the power of compounding. Over short periods the difference from simple interest is small. Over many years it becomes large, because growth builds on earlier growth.
The same mechanism works against you on debt. Unpaid interest on a loan or credit card can be added to the balance and start earning interest itself. See Credit Card Interest and How Loans Work.
Use the calculator to see how a starting amount, a rate, a time period and monthly additions combine:
| Year | You put in | Balance |
|---|---|---|
| 1 | 220,000 | 227,905 |
| 2 | 340,000 | 362,353 |
| 3 | 460,000 | 503,681 |
| 4 | 580,000 | 652,238 |
| 5 | 700,000 | 808,397 |
| 6 | 820,000 | 972,544 |
| 7 | 940,000 | 1,145,090 |
| 8 | 1,060,000 | 1,326,464 |
| 9 | 1,180,000 | 1,517,117 |
| 10 | 1,300,000 | 1,717,524 |
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The compound interest formula
The standard compound interest formula in words:
- Final amount = Principal × (growth factor per period) raised to the power of the number of periods
Where:
- Periodic rate = the yearly rate divided by the number of compounding periods in a year.
- Growth factor per period = the full balance plus the periodic rate on that balance. In other words, each period the balance is multiplied by itself plus its interest.
- Number of periods = the number of compounding periods per year × the number of years.
The interest earned is the final amount minus the principal. The calculator above applies this formula, so you do not need to do the arithmetic by hand.
Why the exponent matters
The number of periods sits in the exponent, not as a simple multiplier. That is why time has more effect than most people expect. Adding years to the period increases the result more than adding the same share to the rate in many cases. Starting earlier usually matters more than starting with a larger amount.
Compounding frequency
Compounding frequency is how often interest is calculated and added to the balance: daily, monthly, quarterly or yearly.
- At the same quoted yearly rate, more frequent compounding gives a slightly higher result, because interest starts earning interest sooner.
- The gain from compounding more often gets smaller as frequency rises. Daily compounding beats monthly compounding by only a small margin.
This is why a quoted yearly rate (the nominal rate) can differ from the effective rate you actually earn or pay over a year. The page APR and Effective Rate explains how to compare offers on the same basis.
Also check whether interest is credited to the balance or paid out to you. If it is paid out and you spend it, there is no compounding. You only get simple interest.
Regular contributions
Most people do not save a single lump sum. They add money every month. Each contribution starts compounding from the date it is added, so:
- Contributions made early in the period have more time to grow than later ones.
- Whether additions come at the start or the end of each month changes the result slightly.
- Over long periods, regular contributions often make up a large part of the final balance, so the habit of adding matters as much as the rate.
The calculator lets you set a monthly addition and shows how much of the final amount comes from your own money and how much from interest.
The rule of 72: a doubling shortcut
The rule of 72 is a quick mental shortcut for how long money takes to double at a fixed yearly compound rate. You divide the constant in the rule's name by the yearly rate in percent, and the answer is roughly the number of years.
It is an approximation. It works reasonably well for moderate rates and becomes less accurate at very low or very high rates. The exact answer comes from logarithms: the doubling time equals the natural logarithm of the doubling factor divided by the natural logarithm of the yearly growth factor.
Compare the shortcut with the exact formula here:
Fill in the empty fields to see the result.
| Annual rate, % | Years to double (rule of 72) | Exact years |
|---|---|---|
| 1% | 72 | 69.66 |
| 2% | 36 | 35 |
| 3% | 24 | 23.45 |
| 4% | 18 | 17.67 |
| 6% | 12 | 11.9 |
| 8% | 9 | 9.01 |
| 10% | 7.2 | 7.27 |
| 12% | 6 | 6.12 |
| 15% | 4.8 | 4.96 |
| 20% | 3.6 | 3.8 |
Rule of 72: years ≈ 72 / rate. Exact: ln 2 / ln(1 + rate), with yearly compounding.
The same shortcut works in reverse for inflation. It shows roughly how long rising prices take to cut the buying power of money sharply. See Inflation and Savings.
What compounding does not tell you
The formula assumes a fixed rate, no withdrawals and no costs. Real life is different:
- Rates change. Bank deposit and savings rates in Pakistan tend to move with the State Bank policy rate. The latest decision on record: SBP policy rate raised by 50 bps to 12% with effect from 27.10.2026 (MPC). For background, see SBP rates and economy.
- Tax and fees reduce the amount that actually compounds. See Payments, tax, Islamic banking.
- Inflation reduces what the final amount can buy. The real return is roughly the nominal return minus inflation.
- Market investments do not compound smoothly. Stocks and funds can fall as well as rise, and a loss reduces the base for later growth. A fixed-rate formula cannot show that risk.
- Islamic products usually pay a profit share rather than interest, so the return is not fixed in advance. See Islamic finance.
Compounding and leveraged trading
Some people apply compounding ideas to trading by reinvesting gains. Leveraged forex and CFD trading can lose money fast, and losses compound too: a deep drawdown needs a much larger percentage gain just to return to the starting balance. A compound calculator shows arithmetic, not an expected outcome. If you trade, read Risk management first. Pakistani readers should also read Law and regulators, because per the SBP, remitting foreign exchange to overseas forex/margin/CFD platforms is not allowed through any payment channel (FERA s.5(1)).
Where to use this next
- Compare deposit products: Deposit Interest and National Savings schemes.
- See how compounding affects borrowing: Effective Loan Rate.
- More tools: Calculators.
- The wider topic: Saving, Investing, Loans.
Frequent questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus interest already added, so the balance grows faster over time.
Does compounding more often make a big difference?
It helps, but the extra gain shrinks as frequency rises. The rate, the time period and regular additions usually matter more than whether compounding is daily or monthly.
How accurate is the rule of 72?
It is a rough estimate that works best at moderate rates. Use the doubling-time calculator on this page to see how far it is from the exact result for your rate.
Can I use a compound interest calculator for stock investments?
Only as an illustration. Stock and fund returns vary from year to year and can be negative. A fixed-rate calculation does not show that risk.
Does compounding work on debt?
Yes. If interest is added to an unpaid balance, you pay interest on interest. This is why credit card and short-term loan balances can grow quickly.
Where do I find current rates?
Use official sources with a date, such as the State Bank of Pakistan for the policy rate, and the bank or scheme provider for the product rate. Rates change, so check the current figure before you decide.