Why compounding accelerates
Simple interest pays a fixed amount each period based only on your original deposit. Compound interest pays interest on your interest, so the base itself grows and each period earns more than the last.
Over short periods the difference is small. Over long ones it dominates. $10,000 at 7% for 30 years earns $21,000 with simple interest, reaching $31,000. With annual compounding it reaches $76,123 — more than double.
The compound interest formula
- A
- Final amount
- P
- Principal — the starting amount
- r
- Annual rate as a decimal
- n
- Compounding periods per year
- t
- Time in years
With regular contributions added, a second term is needed — the future value of an annuity:
- i
- Rate per period — r ÷ n
- N
- Total periods — n × t
- PMT
- Contribution each period
The first term grows your starting lump sum; the second accumulates the contributions. This calculator computes both and adds them.
A worked example
You deposited $130,000 in total, so $170,850 — more than half the final balance — is compound growth.
Does compounding frequency matter?
Less than people expect. Moving from annual to monthly compounding on $10,000 at 7% over 20 years adds about $1,700 to a $38,700 result — roughly 4%. Moving from monthly to daily adds around $50 more.
| Frequency | Effective annual rate | Final balance |
|---|---|---|
| Annually | 7.000% | $38,697 |
| Semi-annually | 7.123% | $39,598 |
| Quarterly | 7.186% | $40,064 |
| Monthly | 7.229% | $40,387 |
| Daily | 7.250% | $40,545 |
The rate itself and the length of time matter far more. A single extra percentage point of return over the same 20 years adds about $8,000 — five times what daily compounding gains you.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal, so it grows in a straight line. Compound interest is calculated on the principal plus all interest previously added, so it grows exponentially.
On $10,000 at 7% for 30 years: simple interest yields $31,000, compound yields $76,123. See the interest calculator to compare both directly.
What return rate should I assume?
For a diversified stock-market portfolio held over decades, 7% after inflation is a common planning figure, based on long-run historical returns. For a mixed stock-and-bond portfolio, 5% to 6% is more conservative. For savings accounts and fixed deposits, use the rate you are actually offered.
Run any long-term plan at a pessimistic rate as well. If it only works at 10%, it is not a plan.
How does inflation affect compound growth?
It erodes what the final number buys. At 3% inflation, $300,000 in twenty years has the purchasing power of about $166,000 today.
Enter an inflation rate in the advanced options to see the result in today's money. This is the number that actually matters for planning.
Is it better to invest a lump sum or contribute monthly?
A lump sum invested earlier is mathematically superior when returns are positive, because more money is exposed to growth for longer. Monthly contributions spread the risk of investing at a bad moment.
Most people do not face this choice — they invest from income as it arrives, which is monthly by nature.
When does compounding really start to matter?
Around year 10 to 15 at typical rates, the interest earned each year begins to exceed what you deposit. That crossover is visible in the year-by-year chart above.
This is why starting early beats contributing more later. $200 a month from age 25 at 7% beats $400 a month from age 40, despite half the total deposits.