How Compound Interest Grows Your Savings: Worked Examples
Automated technical check: . Scope and review policy
Compound interest adds each period's interest to the balance used for the next period. This guide separates a one-time deposit, end-of-month contributions and compounding frequency so that each example can be reproduced without changing its assumptions.
Open the $5,000 worked example in the calculator.
A one-time deposit, step by step
For a fixed nominal annual rate r, n compounding periods per year and t years, the balance is P x (1 + r/n)^(n x t). The rate must be a decimal: 7% is 0.07.
With $5,000, 7% nominal annual interest, 12 monthly periods per year and 20 years, the balance is $20,193.69. There are no additional deposits. The rate is a hypothetical constant, not an expected stock-market return.
Simple interest on the same principal and annual rate adds $350 each year, producing $12,000 after 20 years. Compounding changes the base on which the next interest amount is calculated.
What changes when you contribute each month?
These examples start at zero, deposit $200 at the end of each month and use a fixed 7% nominal annual rate divided by 12. Taxes, fees and inflation are excluded.
| Years | Deposited | Balance | Growth |
|---|---|---|---|
| 10 | $24,000.00 | $34,616.96 | $10,616.96 |
| 20 | $48,000.00 | $104,185.33 | $56,185.33 |
| 30 | $72,000.00 | $243,994.20 | $171,994.20 |
Compare the monthly-deposit example. Beginning-of-month deposits have an additional month of growth per deposit; do not compare balances without adjusting the timing.
Annual, monthly and daily compounding
For $10,000 over 20 years at the same nominal 7% annual rate:
| Periods per year | Balance |
|---|---|
| Annual (1) | $38,696.84 |
| Monthly (12) | $40,387.39 |
| Daily (365) | $40,546.56 |
Daily compounding adds $1,849.71 compared with annual compounding. This holds the nominal rate fixed. Accounts with the same effective annual yield do not gain an extra advantage merely from using a different compounding frequency.
Use a projection without treating it as a promise
Change one assumption at a time: starting balance, monthly deposits, nominal rate or horizon. Include a zero-rate case. A fixed-rate savings illustration is different from an investment portfolio whose returns can be negative and vary from year to year.
The Rule of 72 is only a rough doubling-time shortcut for a positive annual percentage rate. It does not model contributions, fees, variable returns or risk. Use the formula for exact comparisons.
For withdrawals, read how long savings may last. For endpoint growth rather than recurring deposits, see CAGR and effective annual growth.
Common questions
How much does $5,000 become at 7% over 20 years?
At a fixed nominal annual rate of 7% compounded monthly, without additional deposits, the illustrative balance is $20,193.69. This is arithmetic, not a forecast or guaranteed investment return.
Does daily compounding always mean a better account?
At the same nominal 7% rate, $10,000 over 20 years has $1,849.71 more growth with 365 daily periods than annual compounding. Compare effective annual yields, fees, access restrictions and risk rather than frequency alone.
When are monthly deposits made in the calculator?
Deposits are added at the end of each month after interest. The nominal annual rate is divided by 12. Taxes, fees, inflation and changing returns are excluded.
Sources and scope
Examples come from shared calculation functions checked against independent formulas in tests. This is a technical check, not independent financial-professional review.