1. Credit and Debt HS
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Chapter 2
1.
Credit and Debt HS
This lesson will teach you the theory required to fully understand the topic and will present both exercises and selftests to gauge your understanding.
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Lesson Settings & Tools
| | 12 Theory slides |
| | 15 Exercises - Grade E - A |
| | Each lesson is meant to take 1-2 classroom sessions |
Credit and Debt HS
Slide of 12
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
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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.
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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!
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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.
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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
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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.
There is a formula for finding how compound interest affects the balance of a savings account or loan. A = P(1 + r/n)^(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
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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.
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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.
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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?
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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 + r/n)^(nt)
SubstituteValues
Substitute values
A = 1000 (1 + 0.20/12)^(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.
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Loan Interest Rate vs APR
When borrowing money, both the interest rate and the annual percentage rate are important to understand.
Concept
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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
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Layla's Car Loan
Layla takes out a $10 000 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 $10 000 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 + r/n)^(nt)
SubstituteValues
Substitute values
A = 10 000 (1 + 0.05/12)^(12 * 5)
CalcQuotProd
Calculate quotient and product
A = 10 000 (1 + 0.004167)^(60)
AddTerms
Add terms
A = 10 000 (1.004167)^(60)
UseCalc
Use a calculator
A = 12 833.842394...
RoundInt
Round to nearest integer
A ≈ 12 834
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 = 10 000 (1 + 0.06/12)^(12* 5)
▼
Evaluate right-hand side
CalcQuotProd
Calculate quotient and product
A = 10 000 (1 + 0.005)^(60)
AddTerms
Add terms
A = 10 000 (1.005)^(60)
UseCalc
Use a calculator
A = 13 488.501525...
RoundInt
Round to nearest integer
A ≈ 13 489
c We subtract the expected repayment from the actual repayment to find the difference.
$13 489 - $12 834 = $655 Layla will have to pay $655 more than she expected.
Closure
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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.
Credit and Debt HS
Exercise 3.1
Aiden buys a $2500 TV on a 12 months no payments
deal with 18 % interest compounded monthly. He makes no payments during that year.
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Aiden bought a TV for $2500 with an annual interest rate of 18 % compounded monthly. Since he chose a deal where he does not have to make any payments for 12 months, we can calculate the total amount owed after 1 year using the compound interest formula. A = P (1 + rn)^(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.
Aiden owes about $2989 after 1 year.
Now, let's find out how much interest Aiden paid. To do this, we will subtract the original price of the TV from the amount he owes after 1 year.
$2989- $2500 = $489
Aiden paid about $489 in interest.
To avoid paying the extra $489, Aiden could have paid off the full balance before the interest started accumulating. Since the interest was adding up every month, paying off the full balance in the first month would have made it where no interest accrued whatsoever — this is what option C suggests.
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Chloe is considering two car loan offers that are both compounded monthly.
Loan A: & $10 000at6 %APR for4years
Loan B: & $10 000at6 %APR for10years
What are the trade-offs Chloe faces?
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Chloe is choosing between two car loans. Loan A: & $10 000at6 %APR for4years Loan B: & $10 000at6 %APR for10years Both loans have the same APR and the same number of compounding periods. The only difference between them is the length of time. Let's think about what this difference in time will mean to the payments that she will make and the interest that is accrued.
- When a loan lasts longer, the interest has more opportunities to compound which means Chloe will pay more overall. With the 10-year loan, she will pay more interest than with the 4-year loan.
- If Chloe spreads the loan over more time, each monthly payment will be smaller. A 10-year loan breaks the total into many more months, so the monthly payments are lower than with a 4-year loan.
So what is the trade-off? Loan A helps Chloe save money on interest, but she must pay more each month. Loan B makes the monthly payments easier to handle, but the total cost is higher because of the extra interest. Finally, let's evaluate each of the options to see which one accurately describes the situation.
| Option | Explanation | Is It Correct? |
|---|---|---|
| I. She could pay less interest overall and have lower monthly payments. | Lower interest comes from a shorter loan, which means higher monthly payments. | * |
| II. She could pay more interest overall but have lower monthly payments. | A longer loan lowers monthly payments but increases the total interest paid. | ✓ |
| She avoids all interest by choosing the longer loan. | Longer loans increase interest, not remove it. | * |
| IV. There is no difference between the two loans. | The loan length affects both total cost and monthly payments. | * |
The only option that clearly explains the trade-off Chloe faces is option II.
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Marcus is comparing two credit cards.
Card1:& 18 % interest, no annual fee
Card2:& 12 % interest, $100 annual fee
He plans to carry a $500 balance for the year. Which card is more affordable over 12 months?
{"type":"choice","form":{"alts":["Card 1","Card 2"],"noSort":true},"formTextBefore":"","formTextAfter":"","answer":0}
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Marcus is choosing between two credit cards. He plans to carry a $500 balance for 1 year. We will use the compound interest formula to find out which card costs less after 12 months. A = P(1 + r/n)^(nt) In this formula, A is the final amount, P is the principal, r is the annual interest rate written as a decimal, n is the number of times interest is compounded per year, and t is the time in years.
Card 1
This card has 18 % interest and no annual fee, the balance is $500, interest is compounded monthly so n = 12, and the time frame we are considering is 1 year.
Since there is no annual fee, the total cost after one year is $598.
Card 2
This card has 12 % interest and a $100 annual fee, all of the other variables are the same as with Card 1.
Now we need to add the $100 annual fee. $563 + $100 = $663 The total cost after one year is $663.
Conclusion
Card 1 will have a total of $598, and Card 2 will be $663. Card 1 is the better option, because it ends up costing less, even though the interest rate is higher.
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Why is it important to look at the APR and not just the interest rate?
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When you are considering borrowing money, it is essential to understand the costs involved. The interest rate is a crucial factor, but it is not the only thing to look at. We should also look at the APR.
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.
The APR gives us a complete picture of the costs. APR = interest rate + fees The APR does not tell you how much you are borrowing or how long you will be paying off the loan — any principal or length of repayment can have the same APR. Looking at the APR is important since it tells you the true cost of the loan, which corresponds to option C.
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A student got a $1000 loan with 22 % APR, compounded monthly, and didn't make payments for one year. They are shocked by the amount of money that they now owe!
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We know that a student takes out a loan for $1000 with an APR of 22 %. Since the interest is compounded monthly, this yearly rate is spread across 12 months. We will use the compound interest formula to find how much the student will owe after 1 year. A = P (1 + rn)^(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.
At the end of one year, they will owe about $1 244.
They may have thought that a 22 % APR meant they would only pay $220 in interest after one year. But since the interest is compounded monthly, the actual interest paid is more.
What they probably expected:& & What they actually owe: $220 * & & $244 ✓
When interest accrues its own interest, this is called compounding. The student forgot to consider it. This corresponds to option B.
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