Eighth Grade Mathematics: Cost of Credit, Amortization, and Minimum Payments
Borrowing money allows individuals and businesses to make essential major purchases—such as obtaining a college education, buying an automobile, or purchasing a home—before saving the complete cash amount upfront. However, borrowing comes at a substantial price known as the cost of credit. When loans are paid back over long periods with high interest rates, borrowers can end up paying double or triple the original purchase price. In this chapter, you will investigate the true cost of credit cards, understand loan amortization schedules, analyze the financial trap of making minimum payments, and master calculating total loan costs.
The Cost of Credit Defined
Credit is a contractual agreement in which a borrower receives money or goods now and agrees to repay the lender over time with interest and fees:
The Total Cost of Credit Formula:
Total Cost of Purchase = Sum of all Monthly Payments + Down Payment + Fees
Total Interest Paid = Total Cost of Purchase - Original Purchase Price (Principal)
The difference between the total money repaid to the lender and the original cash price is the finance charge, or cost of credit.
Example: Automobile Financing
Car Price: $20,000
Down Payment: $2,000 (Paid in cash upfront)
Loan Amount (Principal): $18,000
Monthly Payment: $360 per month for 60 months (5 years)
Step 1: Calculate total payments made on loan:
$360 * 60 months = $21,600
Step 2: Add down payment to find total cost of vehicle:
Total Cost = $21,600 + $2,000 = $23,600
Step 3: Calculate total interest (finance charge):
Total Interest = $23,600 - $20,000 = $3,600
The borrower paid $3,600 in finance charges for the convenience of spreading the car purchase over 5 years.
The Minimum Payment Trap on Credit Cards
Credit cards are revolving lines of credit with high Annual Percentage Rates (APR), frequently ranging from 18% to 29% per year. Unlike fixed installment loans that end on a set date, credit cards allow consumers to make small minimum monthly payments (often 2% to 3% of the outstanding balance, or a flat $25).
How Credit Card Minimum Payments Work:
Monthly Payment Made ($50)
|
v
+---------------+-----------------+
| Interest Paid | Principal Paid |
| $42 | $8 | <--- Only $8 reduces the actual debt!
+---------------+-----------------+
Because interest is calculated every month on the remaining balance (Monthly Rate = APR / 12), the vast majority of a small minimum payment goes directly toward paying off accumulated interest. Only a tiny fraction reduces the principal balance.
The $3,000 Credit Card Reality at 21% APR:
- If making ONLY minimum payments (starting at $60/month):
Time to Pay Off: Over 17 Years!
Total Interest Paid: Over $4,100!
Total Cost: Over $7,100 for a $3,000 original purchase!
- If paying a fixed $150 per month:
Time to Pay Off: Approximately 25 Months (Just over 2 years!)
Total Interest Paid: Approximately $720
Savings: Over $3,380 in interest saved and 15 years eliminated!
Making only minimum payments traps borrowers in decades of perpetual debt, paying lenders many times the original value of the goods purchased.
Understanding Loan Amortization
An amortized loan (such as a fixed-rate mortgage or car loan) is paid off through equal, regular monthly installments that completely extinguish the debt by the final scheduled payment:
Anatomy of an Amortization Schedule:
Over time, as the principal balance decreases:
- The INTEREST portion of each monthly payment DECREASES.
- The PRINCIPAL portion of each monthly payment INCREASES.
Monthly Payment ($1,000):
Early Years: [======== Interest: $800 ========][== Principal: $200 ==]
Middle Years: [===== Interest: $500 =====][===== Principal: $500 =====]
Final Years: [= Interest: $100 =][========= Principal: $900 =========]
In the early months of a 30-year home mortgage, over 80% of every monthly payment goes strictly toward paying interest; in the final years, over 80% goes toward paying down the principal.
Chapter Exercises
Exercise 1: A consumer buys a 1,200 dollar television using a retail store installment loan. The financing terms require no down payment and 24 monthly payments of 62 dollars each. Calculate the total amount paid for the television, the total finance charge (interest paid), and the percentage markup paid above the original cash price.
Exercise 2: An individual has an outstanding credit card balance of 4,000 dollars with an annual interest rate of 24 percent. Calculate the interest charged for a single month (using monthly rate = 24% / 12). If the cardholder makes a minimum payment of 100 dollars this month, calculate how much money actually reduces the principal debt.
Exercise 3: Explain in paragraph form why extending a loan term from 3 years to 6 years lowers the monthly payment but substantially increases the total cost of the purchase, referencing the mechanics of interest accumulation over time.
Solutions and Explanations
Solution 1: To find the total amount paid for the television, multiply the monthly payment by the number of payments: 24 payments * 62 dollars per month = 1,488 dollars. To calculate the total finance charge (interest paid), subtract the original cash price from the total payments: 1,488 - 1,200 = 288 dollars. To determine the percentage markup paid above the cash price, divide the finance charge by the original price: 288 / 1,200 = 0.24, which equals 24 percent. The consumer pays a total of 1,488 dollars for the television, including 288 dollars in interest, representing a 24 percent cost premium for financing.
Solution 2: To calculate the interest charged for one month on the 4,000 dollar balance at 24% APR, first determine the monthly interest rate by dividing the annual rate by 12: 24% / 12 = 2% per month, which is 0.02 in decimal form. Multiply the balance by the monthly rate to find the month's interest charge: 4,000 * 0.02 = 80 dollars. If the cardholder makes a minimum payment of 100 dollars, that payment is first applied to cover the 80 dollar interest charge: 100 - 80 = 20 dollars. Therefore, only 20 dollars of the 100 dollar payment actually goes toward reducing the principal debt, lowering the outstanding balance to 4,000 - 20 = 3,980 dollars.
Solution 3: Extending a loan repayment term from 3 years (36 months) to 6 years (72 months) lowers the monthly payment because the principal balance is divided across twice as many payment installments. Spreading the repayment across 72 smaller slices makes the monthly budget obligation appear more manageable and affordable. However, this extension substantially increases the total overall cost of the purchase because interest is charged as a continuous percentage fee on the remaining unpaid debt over time. When a loan lasts for 6 years instead of 3, the lender's money remains at risk twice as long, and the principal balance decreases at a much slower pace each month. Consequently, interest is calculated and added to the loan for 72 consecutive months instead of 36. Over those extra three years, the accumulated finance charges mount dramatically, often adding thousands of extra dollars in total interest that far outweigh the temporary convenience of smaller monthly payments.