The formula A equals P times the quantity 1 plus R to the power n calculates the final amount where interest is added to the principal each period and then earns interest itself. This exponential function creates dramatically different outcomes compared to simple interest over long time periods, which is why starting investments early is so powerful. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.
Every repayment on a reducing balance loan does two jobs at once: it pays the interest charged on what you still owe, and whatever's left chips away at the debt itself. Because the balance shrinks each period, the interest shrinks too — so early payments are mostly interest and late ones are mostly principal. Track the balance line by line and the whole topic is just that step, repeated.
Compound interest means interest earns interest because the balance grows each period, calculated using A = P(1 + r)^n where the exponent n makes growth exponential rather than linear.
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