Compound interest calculator
Compound interest adds earned interest back to principal so the next period grows on a larger base. With monthly contributions, time and consistency usually matter more than tiny frequency tweaks.
Use it for savings and long-term investment projections. For short linear notes, see simple interest. To compare advertised nominal rates, use the effective annual rate (EAR/TEA).
With $10,000 starting capital at 7% annual, monthly compounding, $100 monthly contribution for 10 years:
- Final balance: $37,405.09
- Total contributed: $22,000.00 (10,000 + 100 × 12 × 10)
- Interest earned: $15,405.09
Without monthly contributions, the same principal reaches $20,096.61 (interest $10,096.61). The $100/mo habit adds about $17,308.48 of extra wealth.
Formula
A = P × (1 + r/n)^(n×t) + PMT_eq × [((1 + r/n)^(n×t) − 1) / (r/n)]
where: P = principal r = annual rate as decimal (7% → 0.07) n = compounds per year (monthly = 12, quarterly = 4, annual = 1) t = years PMT_eq = contribution per compounding period (monthly contribution × 12/n)
Step-by-step example (defaults)
- P = 10,000 · r = 0.07 · n = 12 · t = 10 · monthly contribution = 100
- Periods = 120 · rate per period ≈ 0.005833
- Compounded principal ≈ $20,096.61
- Future value of contributions ≈ $17,308.48
- Balance = $37,405.09
- Contributed = $22,000 · Interest = $15,405.09
Scenario table (same engine logic)
Rounded to 2 decimals like the calculator. Monthly compounding unless noted.
| Principal | Rate | Years | Monthly contrib. | Final balance | Total contributed | Interest |
|---|---|---|---|---|---|---|
| $10,000 | 7% | 10 | $100 | $37,405.09 | $22,000.00 | $15,405.09 |
| $10,000 | 7% | 10 | $0 | $20,096.61 | $10,000.00 | $10,096.61 |
| $20,000 | 6% | 10 | $150 | $60,969.84 | $38,000.00 | $22,969.84 |
| $5,000 | 10% | 15 | $200 | $105,163.67 | $41,000.00 | $64,163.67 |
| $15,000 | 8% | 20 | $100 | $132,804.08 | $39,000.00 | $93,804.08 |
| $1,000 | 5% | 30 | $50 | $46,080.68 | $19,000.00 | $27,080.68 |
Compounding frequency (no contributions)
$10,000 at 7% for 10 years:
| Frequency | n | Final balance | Interest |
|---|---|---|---|
| Annual | 1 | $19,671.51 | $9,671.51 |
| Quarterly | 4 | $20,015.97 | $10,015.97 |
| Monthly | 12 | $20,096.61 | $10,096.61 |
Monthly vs annual is only about $425 here. Monthly contributions and a longer horizon usually dominate.
Compound vs simple interest
Same $10,000 at 12% for 5 years (compound annual, no contributions):
| Method | Final balance | Interest |
|---|---|---|
| Simple interest (I = P×r×t) | $16,000.00 | $6,000.00 |
| Compound annual | $17,623.42 | $7,623.42 |
| Compound monthly | $18,166.97 | $8,166.97 |
Compounding beats simple by $1,623.42 (annual) or $2,166.97 (monthly). Run the linear case on simple interest.
Rule of 72
72 ÷ rate ≈ years to double (no contributions):
- 8% → ~9 years
- 7% → ~10.3 years
- 6% → 12 years
Handy shortcut; use the calculator for exact contribution paths.
How to combine with other tools
- Size the monthly habit with monthly budget or savings goal.
- Project growth here.
- If debt compounds against you: debt payoff and credit card payment.
- For installment loans: personal loan + amortization + EAR/TEA.
FAQ
Simple interest always uses the original principal. Compound interest adds interest to the base. At $10,000, 12%, 5 years, annual compounding reaches $17,623.42 vs $16,000 simple.
$10,000 at 7% monthly with $100/mo for 10 years → balance $37,405.09, contributed $22,000, interest $15,405.09.
Usually not. Extending the horizon and contributing monthly moves the needle more than switching annual → monthly compounding (~$425 in the 7%/10y example).
72 ÷ rate ≈ years to double without contributions. At 8%, about 9 years. Not a substitute for contribution projections.
Yes. Cards and many loans compound. Prioritize high-rate balances with debt payoff or early loan payoff.
No. Educational projection of compounding and contributions only. Real purchasing power and tax treatment depend on your product and jurisdiction.
Related calculators
- Simple interest
- Effective annual rate (EAR/TEA)
- Savings goal
- Monthly savings
- Monthly budget
- Personal loan
- Amortization schedule
- Debt payoff
- Credit card payment
- Early loan payoff
Educational estimate only. Does not include fees, taxes, inflation, or any guaranteed product return. Confirm terms with your bank or advisor.