Compound interest
Interest paid on both the money you put in and on the interest already added to it, so the balance grows by a larger amount in each period than in the one before.
Simple interest pays on the original sum only, so it adds the same amount every year and the balance climbs in a straight line. Compound interest adds each period's interest to the balance, and the next period pays on that larger balance. Nothing about the rate changes. The base it applies to keeps rising, and that alone bends the line into a curve.
The standard form is , where is the starting balance, the yearly rate, how many times a year interest is added, and the number of years. Rate and time do nearly all the work. Frequency does less than the marketing suggests: at 5 percent, monthly compounding yields 5.116 percent over a year and daily yields 5.127 percent, a difference of about a hundredth of a percentage point. The compound interest calculator shows the shape at any set of inputs.
The mistake is filing compounding under savings. A card balance compounds the same way and usually at a far higher rate, so paying down expensive debt and investing are the same arithmetic seen from opposite ends. The second mistake is comparing two advertised rates without checking how often each one compounds, which is the job APR against APY does.