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The compound interest formula is `A=P(1+r/n)^(nt)` where A is the amount at time t (measured in years for money problems), P is the amount at t=0, r is the rate of growth (interest rate when dealing with money), and n is the number of times compounded per year.
The more often you compound, the higher the rate of return. So in order from lowest to highest return you have annually, semi-annually (every 6 months), and quarterly (every 4 months); this assumes that you start with the same principal P and the same interest rate r, and the same number of years.
If any of the variables differ, it is more difficult to make a blanket statement. For example, is it better to deposit where you get 3% annually, or 2.5% monthly? In general it is better to compound more often, but here a $1000 deposit earns 30$ at 3% for 1 year, while it earns $25.29 at 2.5% compounded monthly.
One hundred dollars compounded annually returns $6.00.
Compounded semiannually it returns $6.09.
Compounded quarterly it returns $6.13 or possibly as much as $6.14 depending on how the bank rounds the numbers.
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