The Vanguard website lists the mutual funds in which one can invest when opening an IRA. Some of those funds have minimum investment amounts of $10,000. Since the annual IRA contribution limits are $5500 / $6500, is the only way to invest in these accounts by rolling over from an existing retirement account an amount that satisfies the minimum investment amount?
Yes, the fund requires a $10,000 minimum investment regardless of how the money gets in to the account. I've found with many custodians there will be multiple variations of the same fund with different minimum investment amounts, and different expense ratios. The same fund may be available with a $1,000 minimum initial investment amount but a slightly higher expense ratio.
If you are opening a new account and want to invest in one of those funds immediately, you can wait until January 1, 2018 and make your $5,500 contributions for 2017 and 2018 at the same time.
Example Vanguard fund with three different variations of expense ratio and minimum entry point.
Expense Ratio: 0.04% Minimum investment: $10,000
Expense Ratio: 0.14% Minimum General Account: $3,000 Minimum UGMA/UTMA: $3,000 Minimum IRA: $3,000 Minimum Education savings: $2,000
Expense Ratio: 0.04% Minimum (current unit price): $226.94
is the only way to invest in these accounts by rolling over from an existing retirement account an amount that satisfies the minimum investment amount?
No. You can also, as quid said, make two years' worth of contributions at once. You can also invest in something else and let your money grow in the IRA; when it grows to over $10,000, you can sell your investments and buy the fund with the $10k minimum. (Selling funds inside the IRA incurs no tax.)