I've been saving money in a high-yield savings account for about 2 years now, and the interest payments felt basically pointless for the first year. But lately I'm noticing the monthly interest is getting noticeably bigger each month. I understand the basic concept that interest earns interest, but I'm curious about the actual math that explains why the growth is so back-loaded.
Compound interest follows an exponential curve, not a linear one, which is why your early payments seemed tiny but now feel meaningful. The reason is pure math: you're earning interest on an increasingly larger base each month. After year one, you might have earned maybe 5% on your original deposit, so the second year's calculations start from a bigger number. It's like a snowball rolling downhill - each rotation picks up more snow, and those later rotations add way more mass than the early ones did.
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