Interest, Compound Growth and the Cost of Borrowing
Interest is the price of using money before you have it, quoted as a rate per year. Because each year's interest earns interest of its own, the same rate turns a long-running debt into a repayment far above the sum borrowed, and a long-held saving into far more than the deposits put in.
What a learner can do afterwards
- Compute a balance after several years of compound interest and compare it against simple interest at the same rate
- Compare two loans by their yearly rate and total repaid rather than by the monthly payment
- Explain why the same rate feels mild over one year and severe over twenty
1 · Read
Compound interest pays interest on past interest, so balances snowball. Leave 100 coins at 10 percent: after year one you hold 110, and year two pays 10 percent of 110, landing at 121, not 120. Each year the base grows, so the yearly gain grows with it. Over decades the curve bends upward hard, which is why starting to save early beats saving bigger but later.
Simple interest pays only on the original sum, so growth stays flat and honest. Put 200 coins at 5 percent simple interest for 3 years and you earn 10 coins a year, 30 in total, ending at 230. The yearly reward never changes because past interest earns nothing extra. Short loans and some bonds work this way for clarity. When terms say simple, the maths stays gentle.
Place the two side by side and compounding always pulls ahead over time. At the same rate, simple interest adds the same slice each year while compound interest adds a growing slice. Over one year they match; over twenty they live on different planets. That is why the same rate feels mild for a year yet severe across decades. Savers should hunt for compounding, borrowers should fear it.
Never shop for a loan by the monthly payment alone. Two loans can share a payment while hiding different yearly rates and very different totals repaid. Compare the yearly rate first, then the full amount you will hand over across the whole term, including fees. A longer term shrinks the monthly bill but fattens the total interest. The cheapest loan has the smallest total cost.
Interest on interest bends the curve, so compare totals, not monthly bills.
2 · Watch
Take it off screen
Where it sits
Where this leads
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.