Start with $10,000, assume 5% compound interest, and make no extra deposits or withdrawals. Under those conditions, the balance first exceeds $20,000 after about 14 years and two months. At the end of year 15, it is about $20,789.
$10,000 at 5% compound interest: year 1 through year 15
This table uses a daily rate equivalent to a 5% annual compound return and shows the balance at the end of each year. The balance is about $19,799 after year 14 and about $20,789 after year 15, so the doubling point falls early in year 15.
| Elapsed time | Balance | Multiple of starting money |
|---|---|---|
| 1 year | About $10,500 | 1.05x |
| 2 years | About $11,025 | 1.10x |
| 3 years | About $11,576 | 1.16x |
| 4 years | About $12,155 | 1.22x |
| 5 years | About $12,763 | 1.28x |
| 6 years | About $13,401 | 1.34x |
| 7 years | About $14,071 | 1.41x |
| 8 years | About $14,775 | 1.48x |
| 9 years | About $15,513 | 1.55x |
| 10 years | About $16,289 | 1.63x |
| 11 years | About $17,103 | 1.71x |
| 12 years | About $17,959 | 1.80x |
| 13 years | About $18,856 | 1.89x |
| 14 years | About $19,799 | 1.98x |
| 15 years | About $20,789 | 2.08x |
Compound interest applies to prior interest too
Compound interest does not apply 5% only to the original $10,000 each year. The first year's $500 of interest joins the balance. The next year's 5% applies to $10,500, and the following year's return applies to the larger balance again.
| Point in time | Calculation | Balance |
|---|---|---|
| After 1 year | $10,000 × 1.05 | $10,500 |
| After 2 years | $10,000 × 1.05² | $11,025 |
| After 3 years | $10,000 × 1.05³ | $11,576.25 |
| After 10 years | $10,000 × 1.05¹⁰ | About $16,289 |
| After 15 years | $10,000 × 1.05¹⁵ | About $20,789 |
The calculator link converts the 5% annual assumption to a 0.013368% daily rate and applies the same mechanism each day. That is why its result closely matches the annual checkpoints above.
At 3%, 5%, and 7%, the doubling time changes
Keep the $10,000 starting balance and $20,000 target fixed, then change only the annual-return assumption.
| Annual-return assumption | When the balance first exceeds $20,000 | Time to double |
|---|---|---|
| 3% | Middle of year 24 | About 23 years and 5 months |
| 5% | Early in year 15 | About 14 years and 2 months |
| 7% | Early in year 11 | About 10 years and 3 months |
The gap between 5% and 7% is two percentage points, but the $20,000 target arrives almost four years earlier. At 3%, it takes more than nine extra years compared with 5%.
Assumptions used in the calculator
| Input | Assumption in this article |
|---|---|
| Starting balance | $10,000 |
| Target balance | $20,000 |
| Annual-return assumption | 5% compound interest |
| Daily rate in the calculator | 0.013368% |
| Deposits and withdrawals | None |
A 5% return is not guaranteed by savings accounts, bonds, funds, or stocks. Fees, taxes, inflation, changing returns, and losing years are outside this example. It shows the time to double under one fixed compound-interest assumption, not an investment recommendation.