Understand this tool
How compound growth works
- What the concept means
- Compound interest is growth calculated on both the original principal and growth already credited to the balance.
- Why it exists
- Estimate how a starting balance and regular deposits could grow when each period’s earnings remain invested.
- When to use it
- Comparing saving amounts, time horizons, assumed annual rates, and compounding frequencies before making a plan.
- What the result means—and does not mean
- Future value combines your total contributions with hypothetical earnings. It is a projection, not a guaranteed investment return.
Why time changes the result
Compounding is recursive: once earnings enter the balance, later periods can earn on them too. Early contributions therefore have more periods in which to grow than late contributions.
APR describes a stated annual rate, while APY or effective annual yield includes within-year compounding. They are not interchangeable when comparing products.
Worked example
A ten-year monthly saving projection
A saver starts with USD 5,000, adds USD 200 per month, and tests a steady 7% annual rate compounded monthly for 10 years.
- Example input
- USD 5,000 initially; USD 200/month; 7% annually; monthly compounding; 10 years.
- Total contributions are 5,000 + (200 × 120) = USD 29,000.
- The monthly periodic rate is 7% ÷ 12, with 120 compounding periods.
- The starting balance and each monthly deposit are grown for the time remaining after that deposit.
- Adding the projected parts gives a future value of about USD 44,665.27.
Example result: Future value ≈ USD 44,665.27; hypothetical earnings ≈ USD 15,665.27.
About 65% of the ending value is contributed money and 35% is hypothetical growth under the fixed-rate assumption.
Key concepts
Key concepts
- Starting principal
- The amount already invested at the beginning of the projection.
- Regular contribution
- The additional amount deposited each month during the projection.
- Annual rate
- The yearly growth assumption entered as a percentage, before fees and taxes.
- Periodic rate
- The annual rate divided across the selected number of compounding periods.
- Compounding frequency
- How often hypothetical earnings are added to the balance.
- Total contributions
- Starting principal plus every regular deposit, without hypothetical earnings.
- Future value
- The projected ending balance after contributions and compounded growth.
- Interest earned
- Future value minus total contributions; this is hypothetical in a projection.
Method or process
Calculation method
Why time changes the result
Compounding is recursive: once earnings enter the balance, later periods can earn on them too. Early contributions therefore have more periods in which to grow than late contributions.
APR describes a stated annual rate, while APY or effective annual yield includes within-year compounding. They are not interchangeable when comparing products.
Formula or rule
FV = P(1 + r/n)^(nt) + contributions grown over their remaining periodsCompare the concepts
The same deposits under three rate assumptions
| Annual assumption | Future value | Hypothetical earnings |
|---|---|---|
| 5% | USD 39,291.50 | USD 10,291.50 |
| 7% | USD 44,665.27 | USD 15,665.27 |
| 9% | USD 50,959.64 | USD 21,959.64 |
Common mistakes
Common mistakes
- Treating a steady entered rate as a promised return.
- Assuming compounding frequency matters more than contribution size and time.
- Ignoring fees, taxes, inflation, withdrawals, and periods of negative performance.
- Calling the full future value “interest” even though it includes contributed money.
Edge cases and limits
Edge cases and limits
- At 0%, the result is simply starting principal plus deposits.
- At 0 years, no future contribution periods are added.
- With no monthly contribution, only the starting balance is projected.
- Very frequent compounding changes the estimate but does not remove market uncertainty.