Talk to your granddaughter's parents first. Ask them what they're planning to do for the child's education. You might need to keep some cash in reserve if there are other potential additions to the family down the road.
If you're thinking of starting with a lump-sum payment, then one attractive option at her young age is a Section 529 prepaid tuition plan. It locks in tuition rates at the time you contribute to the plan. But not all states offer a prepaid tuition plan. You need to understand the financial backing of the state in supporting its plan, what happens if she doesn't go to the school where you thought she might, and the tax benefits associated with contributions and qualified distributions out of the account. Typically, either the account owner or the account beneficiary must be a resident of the state hosting the 529 at the time of enrollment in the plan.
There is also a Private College 529 Plan that doesn't have the residency limitations of a state plan. There are about 270 schools participating in the program.
College cost inflation has been much higher than the general inflation rate. Investing in a prepaid plan offers protection against future tuition increases.
The prepaid plans are attractive because it is otherwise extremely difficult to invest in a college savings plan that will deliver a return that gives you a leg up above the pace of college cost inflation.
If the prepaid tuition plan doesn't work for you, look into 529 college savings plans. In many cases, you don't have to be a resident of the state to open this type of plan, but your home state should be the first place you look for state tax advantages. These can involve contributing to the in-state plan or the benefits of qualified distributions out of the plan.
You need to choose wisely among investment options, annual fees and expenses.
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