Credit, Debt & Compound Interest

You’ll be able to

Explain how credit, interest rates, and credit scores work
Calculate compound interest and describe the power of compounding
Analyze the cost of carrying credit card debt

Credit, interest, and credit scores

Credit is borrowed money you agree to repay, usually with interest — the cost of borrowing, expressed as an annual percentage rate (APR). A credit score is a number (commonly 300–850) that summarizes how reliably you repay debts; it is shaped most by payment history and amounts owed. A high score unlocks lower interest rates on loans and credit cards, so responsible borrowing — paying on time and keeping balances low — literally saves money for decades.

Compound interest: the eighth wonder

Compound interest is interest earned on both the original principal and on previously accumulated interest — interest earning interest. Unlike simple interest, which is calculated only on the principal, compounding accelerates growth over time, so early and consistent saving matters enormously. The same force works against you as a borrower: unpaid credit card interest compounds, making debt balloon. The two great levers of compounding are the interest rate and, above all, time.

The cost of credit card debt

Credit cards charge high APRs (often 20% or more) that compound on unpaid balances, so carrying a balance is expensive. Paying only the minimum payment stretches repayment over years and multiplies the total interest paid. The lesson is symmetrical: compounding builds wealth when you save and invest, but it destroys wealth when you carry high-interest debt. Paying credit cards in full each month avoids interest entirely.

Compound interest

A = P(1 + r)^t

A is the final amount, P the principal, r the annual interest rate (as a decimal), and t the number of years (compounded annually). For compounding n times per year, use A = P(1 + r/n)^(nt).

Worked example

You invest $1,000 at a 6% annual interest rate, compounded annually, and leave it untouched for 3 years. How much will you have, and how much of that is interest? Compare it to simple interest.

1.Apply the compound interest formula: A = P(1 + r)^t = 1,000 × (1 + 0.06)^3.
2.Compute the growth factor: 1.06^3 = 1.06 × 1.06 × 1.06 = 1.191016.
3.Multiply: A = 1,000 × 1.191016 = $1,191.02 (rounded to the cent).
4.Interest earned = $1,191.02 − $1,000 = $191.02. Simple interest would give 1,000 × 0.06 × 3 = $180, so compounding earns about $11 more over just three years — a gap that widens dramatically over decades.

Answer: After 3 years the investment grows to about $1,191.02, of which $191.02 is interest. That beats the $180 simple interest would produce, showing how compounding — interest earning interest — pulls ahead, with the advantage growing larger the longer money stays invested.

Checkpoint

You deposit $2,000 at 5% annual interest compounded annually. Using A = P(1 + r)^t, approximately how much will you have after 2 years?

Watch out

Compounding cuts both ways. The same math that grows your savings makes high-interest debt explode: paying only the minimum on a 20% APR card can take years and cost more in interest than the original purchase. Never underestimate compounding on the debt side.

Checkpoint

Why does starting to save early have such a large effect on the final amount accumulated?

On the exam

For compound interest, substitute carefully into A = P(1 + r)^t: convert the rate to a decimal, apply the exponent (t) before multiplying by P, and subtract the principal if the question asks only for the interest earned rather than the total.

Answer the 2 checkpoints as you read.