Need help figuring out what yearly interest would be?

Even referencing several articles, I can't seem to figure this out; the dividend rate for a savings for instance with \$1,000 says it would be 0.10%, compounded quarterly, to me. That means:

• 1st Quarter it compounds and I get a new balance of \$1,001
• 2nd Quarter it compounds and I get a new balance of \$1,002
• 3rd Quarter it compounds and I get a new balance of \$1,003
• 4th Quarter it compounds and I get a new balance of \$1,004

That means, at the end of the year, I've gained \$4, or 0.40% yield?, so I would assume my APY was 0.40%, but that rate sheet says an APY of 0.10%, does that mean my new balance at the end of the year is supposed be \$1,001 that seems ridiculously wrong.

The mathematical APY calculation here seems to only make it worst, the formula I've seen is (1.00 + dividend rate)^period + 1, that would calculate my APY at which gives me 0.40% APY, which off \$1,000 I would understand to be \$10 or a new balance of \$1,004.

So what is actually happening here? Am I getting \$4 (the APY calculator and manually calculating it, did I do something wrong?) Or the \$1 (which is what it seems the banks interest sheet says)

Either way, both of those seem really low. The interest rate/dividend rate is an annual amount. You can roughly calculate your interest earnings for a single period by dividing the rate by the number compounding periods then multiplying that by the principal balance. For the first period you have principal balance of \$1,000 so the calculation is:

\$1,000 * (0.001/4) = \$0.25

Since this compounds quarterly your second quarter calculation can include the interest earned credited in the first period:

\$1,000.25 * (0.001/4) = \$0.250063

Your compounded interest isn't great enough to beat the rounding error so your second period interest is again \$0.25.

And so on and so forth.

So in a year, your total interest is \$1, which should be somewhat obvious because \$1,000 * 0.001 = \$1, neither the rate nor the principal balance are high enough for the compounding to have any effect.

APY is simply the annual earnings at a given rate considering the frequency of compounding. Compounding is the frequency with which your earned interest is added to your principal balance. At a rate of 0.1% compounding only four times it's reasonable to assume that the annual yield won't be much different from the rate.

((1+(0.001/4))^(4))-1 = 0.1000375%

If it was 0.1% compounded daily you might fare a little better:

((1+(0.001/365))^(365))-1 = 0.10144%

Even then on a principal balance of \$1,000, your interest earnings will be \$1.01 after a year.