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Knowing how loans work is essential before you borrow money. In this lesson, you'll learn the difference between assets and liabilities, how compound interest adds up, and why understanding APR gives you a clearer picture of the true cost of borrowing money.
Catch-Up and Review
Here are a few recommended readings before getting started with this lesson.
Working with decimals:
- Interest rates
- Percentages
Intro to credit:
- Loan
- Borrower and lender
- Principal and interest
Long-term decision-making:
- Impacts of financial decisions over months or years
Saving vs borrowing:
- Understanding that borrowing is not the same as saving
Discussion
Assets and Liabilities
Assets are everything you own that is worth money, like cash, savings, investments, real estate, and valuable items. In other words, an asset is something you own that has value. On the other hand, a liability is something you owe that is a financial obligation.
Explore
Asset or liability?
Sort the items into assets and liabilities. Remember, assets are things that you own that have value and liabilities are things you owe!
Discussion
What Is a Loan?
A loan is money or property that you borrow with a promise to repay the original amount, called the principal, plus extra charges like interest or fees. Loan repayments can be one-time or ongoing.
What kinds of loans are there? Explore the diagram below to discover some common types of loans.
Discussion
Interest Rate
The interest rate is the percentage of the principal a lender charges for borrowing money. It tells you how much the loan will cost over time. The simplest way interest can be calculated is through simple interest. Simple interest is calculated only on the principal amount. There is a formula for finding simple interest.
I=Prt
The variables used in the formula are defined as: - I is the interest earned
- P is the principal amount
- r is the annual interest rate in decimal form
- t is the time spent in years
Discussion
What Is Compound Interest and How Does It Work?
Compound interest is interest that is calculated not just on the original loan or deposit — the principal — but also on the interest already added. This concept is often referred to as interest on interest.
In contrast, simple interest is calculated only on the principal amount.
A=P(1+nr)nt
The variables used in the formula are defined as: - A is the amount of money accumulated after t years, including interest
- P is the principal amount
- r is the annual interest rate in decimal form
- n is the number of times that interest is compounded per year
- t is the time spent paying back the loan in years
Explore
Exploring Simple and Compound Interest
Use the interactive graph to compare simple and compound interest, starting with a $1000 investment and a 5% annual rate. As you explore, notice how the difference between the two types of interest remains small at first but increases over time, illustrating their distinct effects on your investment.
Discussion
Simple and Compound Interest Calculator
Use this calculator to find simple or compound interest. Enter the required parameters for your specific case and choose the interest type to get the result.
Example
Ethan's Credit Card
Ethan buys a gaming laptop for $1000 using a credit card with a 20% annual interest rate, compounded monthly. He was offered a deal where he doesn't have to make any payments for the first year, so he doesn't.
a How much will Ethan owe after 1 year? Round to the nearest whole dollar amount.
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b How much interest did Ethan pay?
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c What could Ethan have done to avoid paying any compound interest?
{"type":"choice","form":{"alts":["Pay off the full balance right away.","Pay the balance off in equal payments over the course of the year.","Buy a cheaper laptop.","Negotiate with the credit card company for better terms and conditions.."],"noSort":false},"formTextBefore":"","formTextAfter":"","answer":0}
d Now imagine that Ethan only used the credit card because he wanted to earn points on the card. He pays off his entire balance before the first bill arrives. How much interest does he pay?
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Hint
a Use the compound interest formula.
b Subtract the original amount he borrowed from the total he owes after one year.
c Think about the fact that the interest compounds each month. What if he pays off the balance in fewer months?
d The interest accrues after each month passes. What happens if there is no debt remaining at the end of the first month?
Solution
a Ethan's initial balance is $1000 and the annual interest rate is 20%, compounded monthly. We calculate the total amount owed after 1 year, where the interest compounds a total of 12 times, using the compound interest formula.
A=P(1+nr)nt
Remember that, in this formula, P is the principal, r is the annual interest rate written as a decimal, n is the compounding periods per year, and t is the time in years.
A=P(1+nr)nt
SubstituteValues
Substitute values
A=1000(1+120.20)12⋅1
CalcQuotProd
Calculate quotient and product
A=1000(1+0.016667)12
AddTerms
Add terms
A=1000(1.016667)12
UseCalc
Use a calculator
A≈1219.40
RoundInt
Round to nearest integer
A≈1219
b The total interest paid is the difference between the total amount paid and the principal.
$1219−$1000=$219
Ethan paid $219 in interest.
c Let's consider the given options to determine what Ethan could have done to avoid paying any compound interest.
| Option | Logic | Conclusion |
|---|---|---|
| Pay off the full balance right away. | No balance remains to accrue interest if paid immediately. | No interest will be paid ✓ |
| Buy a cheaper laptop. | A lower purchase amount reduces total interest but doesn’t prevent it from accruing. | Less interest would be paid overall × |
| Pay the balance off in equal payments over the course of the year. | Interest accrues from the first month, but consistent payments reduce the balance faster. | Less interest would be paid overall × |
| Negotiate with the credit card company for better terms and conditions. | A successful negotiation might lower the interest rate but won't guarantee zero interest. | Less interest might be paid × |
d If Ethan pays the full balance before the first bill arrives, no interest is charged. Ethan will pay $0 in interest.
Discussion
Loan Interest Rate vs APR
When borrowing money, both the interest rate and the annual percentage rate are important to understand.
Concept
Annual Percentage Rate (APR)
The annual percentage rate (APR) represents the annual cost of borrowing money, shown as a percentage. It includes the interest rate plus any extra fees or costs associated with the loan.
Banks often advertise the interest rate instead of the APR because it's more attractive. This is because the interest rate only shows the cost of borrowing, while the APR includes interest plus fees. APR is usually higher and gives a more complete picture of the total cost of a loan. By highlighting the lower interest rate, banks make their loans appear more appealing.
Example
Layla's Car Loan
Layla takes out a $10000 loan to buy her first car. She is told that the interest rate is 5%, compounded monthly, and she plans to pay it off in 5 years. She uses this number to build her budget. After reviewing her contract, she learns that there are extra fees included in the loan, which brings the annual percentage rate (APR) to 6%.
a How much did Layla think her total repayment would be (based on 5% interest)? Round to the nearest whole dollar amount.
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b What is the actual total cost of the loan (based on 6% APR compounded monthly)? Round to the nearest whole dollar amount.
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c What is the difference between what she expected to pay and what she actually has to pay?
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Hint
a Use 5% as the interest rate in the compound interest formula.
b Use 6% as the interest rate now.
c Subtract the expected total from the actual total.
Solution
a We want to calculate the total repayment Layla expected for her $10000 loan based on a 5% interest rate compounded monthly — which means that it happens 12 times every year — for 5 years. Let's recall the formula for compound interest.
A=P(1+nr)nt
In this formula, P is the principal, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and t is the number of years.
A=P(1+nr)nt
SubstituteValues
Substitute values
A=10000(1+120.05)12×5
CalcQuotProd
Calculate quotient and product
A=10000(1+0.004167)60
AddTerms
Add terms
A=10000(1.004167)60
UseCalc
Use a calculator
A=12833.842394…
RoundInt
Round to nearest integer
A≈12834
b Now we calculate the actual repayment using the APR of 6% compounded monthly. Everything about the compound interest formula will remain the same except that r is now 0.06.
A=10000(1+120.06)12×5
▼
Evaluate right-hand side
CalcQuotProd
Calculate quotient and product
A=10000(1+0.005)60
AddTerms
Add terms
A=10000(1.005)60
UseCalc
Use a calculator
A=13488.501525…
RoundInt
Round to nearest integer
A≈13489
c We subtract the expected repayment from the actual repayment to find the difference.
$13489−$12834=$655
Layla will have to pay $655 more than she expected.
Closure
Why Understanding Loans, Interest, and APR Matters
Loans can help you pay for important things — like a car, college tuition, or even a home — but only if you understand how they really work.
When you borrow money, you're not just paying back the amount you took out — you're actually paying back extra money in the form of interest and possibly fees. That's why it's so important to know:
- What the loan amount is (the principal)
- How often interest is added (compound interest grows faster than simple interest)
- What the APR is (because it shows the true cost of the loan, not just the interest rate)
If you don't read the fine print or don't understand these terms, you could:
- End up in more debt than you expected
- Struggle to make payments
- Hurt your credit score, which affects your ability to borrow in the future
- Pay hundreds or even thousands of dollars more than planned
Understanding loans now helps you make smarter financial decisions later, so you're in control of your money — instead of your money controlling you.
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