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Question #56277 posted on 03/04/2010 3:01 a.m.

Dear 100 Hour Board,

Let's say you have a set amount of money and you put it in a high-yield savings account, like ING Direct. ING lets you create subaccounts, which are basically different savings accounts for whatever needs you have. Like, you could have a college education account, a car fund account, a down payment for a house account, etc. My question is this: will you make the same amount of interest putting the money in separate accounts as opposed to keeping it all in one savings account? Or will you end up making more money by keeping it all together?

~ Lady Bug

A: Dear Lady Bug,

Go right ahead and use those subaccounts. It makes no difference at all to the interest you earn. The math is pretty simple, too, if you know what formula to start with.

First of all, here's the formula for compound interest:

Formula for compound interest.

A is the amount in the account after a given period of time, P is the starting principal, r is the annual interest rate, n is how often (per year) the interest is compounded, and t is the number of years. However, you don't even need to worry about most of that, for this answer; everything except for P is going to stay the same in the following steps.

Now, to answer your question, let's say you split your money into two amounts, P1 and P2, such that P1 + P2 = P. Now, let's look how much total money you'll have at some later time, with the money split into two accounts:

Set of equations showing that the total money will be the same as if it hadn't been split.

Notice how we got the initial formula back? In other words, it doesn't matter at all how you split it up: since the interest rate, length of time, and how often the money is compounded all stay the same for the subaccounts, things work out the same as if all the money were in one account.

—Laser Jock