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WalletPrep worksheet · Debt

How does loan amortization work?

Name ____________________ Date __________

Key ideas

  1. Interest is charged on what you still owe. Each month's interest is the balance × the yearly rate ÷ 12. A smaller balance means less interest.
  2. Early payments are mostly interest. Leo's first payment of $396.02 is $116.67 interest and $279.35 principal. His last is $2.30 interest.
  3. Extra principal early saves the most. Adding $50 a month to Leo's loan saves about $508 in interest and ends it 7 months sooner.

Vocabulary

Principal
The amount you borrowed, or the part of your balance that is still owed, not counting interest.
Amortization
Paying off a loan with equal payments over time, where early payments are mostly interest and later ones are mostly principal.
Minimum payment
The smallest amount you must pay on a credit card or loan by the due date to keep the account in good standing.
APR
Annual percentage rate: the yearly cost of borrowing money, shown as a percentage. It is the number to compare on cards and loans.

Work it out

Leo borrows $20,000 for a car at 7% APR for 60 months. His payment is $396.02. Here is how his first payment splits.

  1. Monthly payment
  2. Month 1 interest ($20,000 × 7% ÷ 12)
  3. Principal paid in month 1
  4. Starting balance
  5. Principal paid
  6. Balance after month 1
  7. Month 60 interest
  8. Total interest over 60 months

Check yourself

  1. A loan has a $12,000 balance at 6% APR. How much interest is charged this month?

    • A. $6
    • B. $60
    • C. $72
    • D. $720

  2. On a fixed-rate amortizing loan, what happens to the interest part of each payment over time?

    • A. It grows
    • B. It stays the same
    • C. It shrinks

  3. When does an extra principal payment save the most interest?

    • A. Early in the loan
    • B. Halfway through
    • C. In the last year
    • D. It saves the same at any time

Your turn

Log in to one of your loans and find your balance, rate and payment. Work out this month's interest as balance × rate ÷ 12, and see how much of your payment actually lowers the balance.

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Answer key

How does loan amortization work?

Work it out

  1. Monthly payment$396.02
  2. Month 1 interest ($20,000 × 7% ÷ 12)− $116.67
  3. Principal paid in month 1= $279.35
  4. Starting balance$20,000
  5. Principal paid− $279.35
  6. Balance after month 1= $19,720.65
  7. Month 60 interest$2.30
  8. Total interest over 60 months$3,761
  1. Month 1 interest is $20,000 × 7% ÷ 12 = $116.67. The rest of the payment, $396.02 − $116.67 = $279.35, lowers the balance.
  2. The new balance is $20,000 − $279.35 = $19,720.65. Month 2 interest is figured on that smaller balance, so it drops to $115.04.
  3. By month 60 the interest is just $2.30. Across all 60 payments Leo pays about $3,761 in interest on top of the $20,000.

Check yourself

  1. B. $60 $12,000 × 6% ÷ 12 = $60. Monthly interest is the balance times the APR divided by 12.
  2. C. It shrinks Interest is charged on the balance, which falls each month, so the interest part shrinks and the principal part grows.
  3. A. Early in the loan Paying early cuts the balance that every later month's interest is charged on, so the savings repeat for more months.