How to Understand Cost of Credit and Loans? (+FREE Worksheet!)

When you borrow money, whether through a credit card, a car loan, or a student loan, the lender charges you extra for the privilege of using their money. That extra charge is called interest, and it can turn a seemingly affordable purchase into something much more expensive. Understanding the cost of credit and loans is one of the most important financial skills an 8th grader can develop.

Think of interest as a rental fee: you are renting someone else’s money, and the longer you keep it, the more rent you pay. Two key factors determine how much interest you owe, the interest rate and the loan term (how many years you borrow for). A higher rate or a longer term always means more interest paid overall.

Key Formulas for Credit and Loans

Most loan calculations in 8th-grade math use one of two formulas:

• Simple Interest: \(I = P \cdot r \cdot t\), where \(P\) is the principal (amount borrowed), \(r\) is the annual interest rate (as a decimal), and \(t\) is the time in years.
• Compound Interest: \(A = P(1 + r)^t\), where \(A\) is the total amount owed after \(t\) years.
• Total Repayment: Principal + Total Interest

Simple interest grows at a constant rate, the same dollar amount each year. Compound interest charges interest on top of previously accumulated interest, so the balance grows faster over time. Credit cards almost always use compound interest, which is why unpaid balances can snowball quickly.

How Interest Rate and Loan Length Affect Cost

Consider borrowing \(\$5{,}000\). At 4% simple interest for 3 years, the interest is \(5{,}000 \times 0.04 \times 3 = \$600\). But at 8% for 3 years, the interest doubles to \(\$1{,}200\). Doubling the rate doubles the cost.

Now look at loan length: \(\$4{,}000\) at 5% for 3 years costs \(4{,}000 \times 0.05 \times 3 = \$600\) in interest. Stretch that to 5 years and the interest jumps to \(4{,}000 \times 0.05 \times 5 = \$1{,}000\). The longer loan costs \(\$400\) more even at the same rate.

Comparing Loan Types

Step-by-Step Examples

Example 1, Simple Interest: Short vs. Long Loan

Compare borrowing \(\$4{,}000\) at 5% simple interest for 3 years versus 5 years.

Solution:

• 3-year interest: \(I = 4{,}000 \times 0.05 \times 3 = \$600\). Total repaid: \(\$4{,}600\).
• 5-year interest: \(I = 4{,}000 \times 0.05 \times 5 = \$1{,}000\). Total repaid: \(\$5{,}000\).

The longer loan costs \(\$400\) more in interest.

Example 2, Compound Interest on a Credit Card

You charge \(\$800\) on a credit card at 20% annual compound interest and make no payments for 2 years. How much do you owe?

Solution: \(A = 800(1.20)^2 = 800 \times 1.44 = \$1{,}152\).

You owe \(\$352\) extra in interest alone.

Example 3, Comparing Two Interest Rates

Borrow \(\$2{,}000\) for 4 years. Bank A charges 6% simple; Bank B charges 10% simple.

Solution:

• Bank A: \(I = 2{,}000 \times 0.06 \times 4 = \$480\). Total: \(\$2{,}480\).
• Bank B: \(I = 2{,}000 \times 0.10 \times 4 = \$800\). Total: \(\$2{,}800\).

A 4-percentage-point higher rate costs an extra \(\$320\).

Video Lesson

Watch this video for additional examples and a step-by-step walkthrough:

Practice Problems

1. \(P = \$3{,}000\), \(r = 5\%\), \(t = 2\) years. Find the total repayment (simple interest).
2. \(P = \$3{,}000\), \(r = 5\%\), \(t = 5\) years. Find the total repayment.
3. \(P = \$5{,}000\), \(r = 4\%\), \(t = 3\) years. Find the interest.
4. \(P = \$5{,}000\), \(r = 8\%\), \(t = 3\) years. Find the interest.
5. \(P = \$1{,}500\), \(r = 18\%\), \(t = 1\) year. Find the total repayment.
6. \(P = \$1{,}500\), \(r = 6\%\), \(t = 1\) year. Find the total repayment.
7. \(P = \$600\), \(r = 20\%\) compound, \(t = 2\) years. Find \(A\).
8. \(P = \$600\), \(r = 20\%\) simple, \(t = 2\) years. Find the total.
9. Marcus borrows \(\$6{,}000\) for a car. Bank A offers 5% simple for 3 years; Bank B offers 4% simple for 5 years. Which costs less total interest?
10. Layla puts \(\$500\) on a credit card at 24% compound interest and makes no payments for 3 years. How much does she owe?

Solutions

1. \(I = 3{,}000 \times 0.05 \times 2 = \$300\). Total = \(\$3{,}300\).
2. \(I = 3{,}000 \times 0.05 \times 5 = \$750\). Total = \(\$3{,}750\). Three extra years cost \(\$450\) more.
3. \(I = 5{,}000 \times 0.04 \times 3 = \$600\).
4. \(I = 5{,}000 \times 0.08 \times 3 = \$1{,}200\). Double the rate doubles the interest.
5. \(I = 1{,}500 \times 0.18 \times 1 = \$270\). Total = \(\$1{,}770\).
6. \(I = 1{,}500 \times 0.06 \times 1 = \$90\). Total = \(\$1{,}590\). Lower rate saves \(\$180\).
7. \(A = 600(1.20)^2 = 600 \times 1.44 = \$864\).
8. \(I = 600 \times 0.20 \times 2 = \$240\). Total = \(\$840\). Compound cost \(\$24\) more.
9. Bank A interest: \(6{,}000 \times 0.05 \times 3 = \$900\). Bank B interest: \(6{,}000 \times 0.04 \times 5 = \$1{,}200\). Bank A costs \(\$300\) less.
10. \(A = 500(1.24)^3 \approx 500 \times 1.9066 = \$953.31\). She owes about \(\$953\); roughly \(\$453\) is interest.

Real-World Applications

Car Loans: A \(\$10{,}000\) car loan at 6% simple interest for 5 years costs \(\$3{,}000\) in interest, bringing the true price to \(\$13{,}000\). Monthly payments would be about \(\$216.67\).

Credit Card Minimum Payments: Paying only the minimum on a \(\$2{,}000\) balance at 18% can result in over \(\$3{,}000\) in total interest and take more than 8 years to pay off. Always pay more than the minimum!

Common Mistakes to Avoid

• Focusing only on the monthly payment. A lower monthly payment over a longer term often costs much more in total interest.
• Forgetting that compound interest grows on itself. A 20% compound rate costs more than 20% simple over the same period.
• Ignoring payday-loan rates. Rates above 300% can turn a small loan into a massive debt trap.

Study Tips

• Always calculate total interest paid, not just whether you can afford the monthly payment.
• Credit cards charge interest on the unpaid balance. Paying the full balance each month means \(\$0\) in interest.
• The golden rule: Borrow as little as possible, at the lowest rate, for the shortest time.

Frequently Asked Questions

What is the cost of credit on a loan?

The cost of credit is the extra money you pay to borrow, mostly interest plus any fees. With simple interest, I = P × r × t. Borrowing $5,000 at 4% for 3 years costs 5,000 × 0.04 × 3 = $600 in interest, so you repay $5,600 in total. A higher rate or a longer loan always raises that cost.

What is the cost of credit called?

The cost of credit is usually called the finance charge. It is the total dollar amount you pay to borrow, including interest and certain fees. For example, if you borrow $4,000 and repay $4,600, the finance charge is $600. Lenders also show the cost as a yearly rate so you can compare loans of different sizes.

What is the cost of credit expressed as?

The cost of credit is expressed as an annual percentage rate, or APR, along with the finance charge in dollars. The APR turns interest and fees into one yearly rate, which makes loans easier to compare. A loan at 5% APR costs less each year than the same loan at 8% APR, and that gap grows the longer you borrow.

Is a bank loan cheaper than a credit card?

A bank loan is often cheaper than carrying a credit card balance, because personal loans usually have lower interest rates and a fixed payoff date. Credit card interest compounds, so an unpaid balance can snowball. The real answer depends on the rates and fees you are offered, so compare the total amount you would repay with each option.

Is it cheaper to get a loan to pay off credit cards?

It can be cheaper if the loan has a lower interest rate than your cards and small fees, and if you stop adding new card debt. Compare the total interest both ways. For example, $4,000 at 5% simple interest for 3 years costs $600, while the same balance at a much higher card rate would cost far more over the same time.

What is an example of the cost of credit?

Suppose you borrow $4,000 at 5% simple interest. Over 3 years the interest is 4,000 × 0.05 × 3 = $600, but over 5 years it is 4,000 × 0.05 × 5 = $1,000. Same rate, longer term, $400 more in interest. That extra $400 is part of the cost of credit, and it shows why shorter loans usually cost less.