Compound Interest Calculator
Project growth with compounding periods, interest rate, and time horizon. Interest is added to the balance, so later periods earn interest on earlier interest.
Result
Final investment value
$31,998.32
- Money invested
- $22,000.00
- Interest earned
- $9,998.32
- Initial principal
- $10,000.00
- Contributions
- $12,000.00
Effective annual yield: 5.11619%. This is not the nominal annual rate entered above.
A = P × (1 + r / n) ^ (n × t), with contributions added on their own schedule
- The nominal annual rate is 5%, or 0.05 as a decimal. Dividing by 12 compounding periods gives a periodic rate of 0.00416667.
- The duration is 10 years, which is 10 years and 120 compounding periods.
- The principal of 10000 grows by (1 + 0.00416667) raised to the number of compounding periods that have occurred.
- 120 monthly contributions of 100 are added at the end of each contribution period. Interest is credited on the compounding dates, not on the contribution dates.
- The effective annual yield at this compounding frequency is 5.11619%. That is not the same figure as the nominal annual rate.
- Final value 31998.32. Money invested 22000. Interest earned 9998.32. The rate stays constant, and the result excludes taxes, inflation, and fees.
Interest compounds on the selected schedule. Contributions are added on their own schedule, at the beginning or end of each contribution period. When both happen at the same moment, interest is credited first. Money added between compounding dates earns interest at the next compounding date, including a partial final period.
Investment growth
Year-by-year balance
| Period | Deposits | Interest | Ending balance | Total invested |
|---|---|---|---|---|
| Year 1 | $1,200.00 | $539.50 | $11,739.50 | $11,200.00 |
| Year 2 | $1,200.00 | $628.50 | $13,568.01 | $12,400.00 |
| Year 3 | $1,200.00 | $722.05 | $15,490.06 | $13,600.00 |
| Year 4 | $1,200.00 | $820.39 | $17,510.44 | $14,800.00 |
| Year 5 | $1,200.00 | $923.75 | $19,634.20 | $16,000.00 |
| Year 6 | $1,200.00 | $1,032.41 | $21,866.60 | $17,200.00 |
| Year 7 | $1,200.00 | $1,146.62 | $24,213.23 | $18,400.00 |
| Year 8 | $1,200.00 | $1,266.68 | $26,679.91 | $19,600.00 |
| Year 9 | $1,200.00 | $1,392.88 | $29,272.79 | $20,800.00 |
| Year 10 | $1,200.00 | $1,525.54 | $31,998.32 | $22,000.00 |
Worked examples
Example 1
$10,000 at 5% for 10 years
Compounded monthly, the periodic rate is 0.05 / 12. After 120 periods the balance is $16,470.09. No contributions are added, and the nominal 5% rate is not the effective annual yield.
Example 2
$1,000 at 10% for 2 years
Compounded annually, the first year ends at $1,100.00 and the second at $1,210.00. Interest in the second year is earned on both the principal and the first year's interest.
Example 3
Monthly deposits, quarterly interest
A $1,000.00 start plus $100.00 at the end of each month, with 12% compounded quarterly, finishes at $2,405.70. Deposits made between compounding dates earn interest at the next compounding date.
How compound interest is calculated
A lump sum uses A = P(1 + r/n)^(nt). P is the initial amount, r is the nominal annual rate as a decimal, n is the number of compounding periods in a year, and t is the time in years. Months are treated as twelfths of a year, so 18 months is t = 1.5.
Common questions
Does the annual rate mean the effective annual yield?
No. The rate you enter is a nominal annual rate. It is divided by the number of compounding periods. The effective annual yield is (1 + r/n)^n − 1 and is shown separately.
How are contributions timed when compounding uses a different schedule?
Interest compounds on the selected schedule. Contributions are added on their own schedule, at the beginning or end of each contribution period. When both happen at the same moment, interest is credited first. Money added between compounding dates earns interest at the next compounding date, including a partial final period.
Does changing the currency convert the amount?
No. The currency control changes the symbol and the way the number is grouped. A balance of 10000 is still 10000 after you switch from USD to EUR.
Are negative interest rates allowed?
Yes, when every compounding period keeps a positive growth factor. A rate that would make 1 + r/n zero or negative is rejected because the fractional-period calculation would not be a real number.
Do the results include taxes, inflation, or fees?
No. The projection assumes the nominal rate stays constant for the whole duration. Taxes, inflation, and fees are not deducted.