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Financial Literacy
How Loans Are Repaid Over Time
Amortization and the principal-interest split
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A loan lets a person borrow money now and pay it back over time. The amount borrowed is called the principal, and the lender charges interest as the cost of using that money. Many loans, such as car loans, mortgages, and student loans, are repaid with fixed monthly payments. Understanding how each payment works helps students compare loans and avoid paying more than expected.
Key Facts
- Monthly interest rate = annual interest rate / 12
- For a $10,000 loan at 6% annual interest, the monthly interest rate is 0.06 / 12 = 0.005, or 0.5%
- Fixed monthly payment formula: M = P(r(1 + r)^n) / ((1 + r)^n - 1)
- For 193.33 per month for 60 months
- First month interest = 10000 x 0.005 = 193.33 - 143.33
- Total paid is about 11,599.80, so total interest is about $1,599.80
Vocabulary
- Principal
- Principal is the original amount borrowed or the remaining loan balance that still needs to be paid back.
- Interest
- Interest is the extra money paid to a lender as the cost of borrowing money.
- Amortization
- Amortization is the process of paying off a loan over time with payments that cover both interest and principal.
- Fixed monthly payment
- A fixed monthly payment is a payment amount that stays the same each month during the loan term.
- Loan term
- The loan term is the length of time the borrower has to repay the loan.
Common Mistakes to Avoid
- Thinking the same amount of interest is paid every month. This is wrong because interest is based on the remaining balance, which gets smaller over time.
- Confusing payment amount with principal paid. A loan payment includes both interest and principal, so only part of the payment reduces the balance.
- Using the annual interest rate as the monthly interest rate. This is wrong because monthly loan calculations usually use annual rate / 12.
- Assuming a lower monthly payment always means a cheaper loan. A longer term can lower the monthly payment but increase the total interest paid.
Practice Questions
- 1 A $10,000 loan has a 6% annual interest rate. What is the monthly interest rate as a decimal and as a percent?
- 2 Using a fixed monthly payment of 10,000 loan at 6% annual interest.
- 3 In an amortized loan with a fixed payment, why does the principal part of each payment usually increase over time while the interest part decreases?