$100,000 needs an annual compound return of about 7.1773% to reach $200,000 in 10 years, with no deposits or withdrawals.
Start with $100,000, make no additional deposits, and leave the money invested for 10 years. To finish with $200,000, the balance needs to compound at about 7.1773% a year.
Why 7% falls just short
A return that stays constant for a decade produces the following outcomes.
| Annual return | Balance after 10 years | Investment gain |
|---|---|---|
| 3% | About $134,392 | About $34,392 |
| 5% | About $162,889 | About $62,889 |
| 7% | About $196,715 | About $96,715 |
| 7.1773% | About $200,000 | About $100,000 |
| 8% | About $215,893 | About $115,893 |
At 7%, the account ends about $3,285 below the $200,000 target. At 8%, it ends about $15,893 above it. The return needed to land on the target lies between those two rates.
The 10-year path to $200,000
If the 7.1773% return repeats each year, the year-end balance grows like this.
| Elapsed time | Balance | Multiple of starting money |
|---|---|---|
| 1 year | About $107,177 | 1.07x |
| 2 years | About $114,870 | 1.15x |
| 3 years | About $123,114 | 1.23x |
| 4 years | About $131,951 | 1.32x |
| 5 years | About $141,421 | 1.41x |
| 6 years | About $151,572 | 1.52x |
| 7 years | About $162,450 | 1.62x |
| 8 years | About $174,110 | 1.74x |
| 9 years | About $186,607 | 1.87x |
| 10 years | $200,000 | 2.00x |
The first year's gain is about $7,177. During the tenth year, the same rate applies to a much larger balance, adding about $13,393. Compounding increases the amount on which the next return is earned.
Calculating the required return
The equation is `$100,000 × (1 + annual return)¹⁰ = $200,000`. Because the target is twice the starting balance, the required annual return is the tenth root of 2 minus 1, or about 7.1773%.
The dollar amount does not change the rate needed to double. Turning $10,000 into $20,000 or $1 million into $2 million over the same 10 years requires the same annual compound return.
More time lowers the annual return required to reach 2x.
| Time allowed to double | Required annual compound return |
|---|---|
| 5 years | About 14.8698% |
| 10 years | About 7.1773% |
| 15 years | About 4.7294% |
| 20 years | About 3.5265% |
| 30 years | About 2.3374% |
Assumptions
| Input | Assumption |
|---|---|
| Starting balance | $100,000 |
| Target balance | $200,000 |
| Time | 10 years, or 3,650 days |
| Required annual compound return | About 7.1773% |
| Daily compound rate used by the calculator | About 0.018992% |
| Deposits and withdrawals | None |
This is a simplified compounding simulation with a constant return. It excludes taxes, fees, inflation, market volatility, and losing periods. It does not promise a 7.1773% return or recommend any investment.