Compound Interest Formula Explained
The standard compound interest formula is useful for lump sums. Recurring deposits need extra care because each deposit compounds for a different amount of time.
Variables
| Symbol | Meaning | Example |
|---|---|---|
| A | Final amount | $19,672 |
| P | Starting principal | $10,000 |
| r | Annual interest rate as decimal | 0.07 |
| n | Compounding periods per year | 12 for monthly |
| t | Years | 10 |
Quick formula calculator
What the basic formula does not cover
- Monthly deposits. Use the monthly contributions calculator for recurring deposits.
- Taxes and fees. Lower the assumed return if you need a rough after-fee estimate.
- Inflation. Use today’s dollars or real return pages for purchasing-power thinking.
Related pages
FAQ
What is the compound interest formula?
A = P × (1 + r/n)nt.
Can I use this formula for monthly savings?
Not directly. Monthly savings need an annuity formula or calculator logic.
Why is n important?
n controls how many times per year interest is applied.
Worked example: $10,000 at 7% for 30 years
The compound interest formula is A = P(1 + r/n)nt, where P is the principal, r the annual rate, n the times it compounds per year and t the number of years. With P = $10,000, r = 0.07, n = 1 and t = 30: A = 10,000 × (1.07)30 = $76,123. Only $10,000 was invested — the rest is interest earning interest.
Principal $10,000 + interest $66,123. Educational estimate, not financial advice.
| Year | Balance | Of which interest |
|---|---|---|
| 0 | $10,000 | $0 |
| 5 | $14,026 | $4,026 |
| 10 | $19,672 | $9,672 |
| 15 | $27,590 | $17,590 |
| 20 | $38,697 | $28,697 |
| 25 | $54,274 | $44,274 |
| 30 | $76,123 | $66,123 |
What each part of the formula does
| Symbol | Meaning | In the example |
|---|---|---|
| P | Principal (starting amount) | $10,000 |
| r | Annual interest rate (decimal) | 0.07 (7%) |
| n | Compounds per year | 1 (yearly) |
| t | Number of years | 30 |
| A | Final amount | $76,123 |
Compound interest formula: common questions
How do you calculate compound interest?
Use A = P(1 + r/n)^(nt). Multiply the principal by one plus the periodic rate, raised to the number of periods, then subtract the principal to get interest alone.
What is the formula with monthly compounding?
Use n = 12: A = P(1 + r/12)^(12t). Compounding monthly grows slightly faster than yearly at the same annual rate.
How do I add regular contributions?
Add the future value of the deposits; each contribution also earns compound interest. A monthly-contribution calculator handles the lump sum and deposits together.
Why does the balance curve bend upward?
Because each year's interest is added to the balance and then earns interest itself — that 'interest on interest' makes the line steepen over time.