Compound Interest

Pre-Calculus · Axiom Academy

Why money left to grow earns interest on its own interest — and how the formula captures it. 1. Simple vs. Compound Interest Put 1,000 in two accounts, both paying 5% a year . The simple-interest account adds a flat 50 every year — interest only on the original 1,000 . The compound account adds 5% of the current balance, so it pulls steadily ahead as it starts earning interest on its interest. 2,000 — the principal plus 20 flat 50 payments. 2,653.30 — about 653 more, over 30% extra, all from compounding. One equation handles any rate and any compounding schedule: The starting amount you invest or borrow. The yearly interest rate, written as a decimal (6% means r = 0.06 ). How many times interest is added each year (monthly is n = 12 ). How long the money is left to grow. The animation builds the two pieces that do the work: the per-period growth factor , raised to the total number of periods nt . 3. A Worked Example — Monthly Compounding You invest 5,000 at 6% annual interest, compounded monthly, for 10 years . How much will you have? Substitute P = 5000 , r = 0.06 , n = 12 , t = 10 into the formula and simplify. The animation climbs the balance year by year — each step adds that year's interest on top of everything earned so far, ending exactly at the answer. Your 5,000 grows to about 9,096.98 — nearly doubling in 10 years. 4. Why More Frequent Compounding Helps

This is the written version of the interactive lesson above. See the full Pre-Calculus course.