doing math

courses › Finance & Money

Loans & Amortization

level 34 course

Monthly interest, how each payment splits, and what a loan really costs.

Pen and paper is fine · no calculator needed why?

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the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

A loan payment does two jobs. First it pays this month's interest: the balance times the monthly rate. The rest of the payment reduces the principal, the amount you still owe. Paying a loan down this way, month by month, is called amortization.

Interest is charged on the balance, so it shrinks as the balance shrinks, and later payments pay off more principal.

Over the whole loan, the interest you pay is everything you repay minus what you borrowed.

Techniques

Interest first, then principal

One monthly payment on a loan.

  1. Interest is the balance × the monthly rate. 1.5% is 0.015.
  2. Principal repaid is the payment minus the interest.
  3. The new balance is the old balance minus the principal repaid.
worked example

Example: A bakery's loan begins the month at $12,000. Assume interest is 1% for the month, and a payment of $500 is made at month-end. What is the ending principal balance?

  1. Interest: $12,000 × 0.01 = $120.
  2. Principal repaid: $500 − $120 = $380.
  3. Ending principal: $12,000 − $380 = $11,620.

Answer: $11,620

Repeat the month

Two payments in a row.

  1. Add this month's interest to the balance, then take off the payment.
  2. Start the next month from that new balance.
  3. Work out the interest again. It is smaller now.
worked example

Example: You owe $5,000 on a loan. Assume it charges 2% interest per month: each month, interest is added on the balance, then your $500 payment comes off. What is the balance after two payments?

  1. Month 1: $5,000 + $100 − $500 = $4,600.
  2. Month 2: $4,600 + $92 − $500 = $4,192.

Answer: $4,192

Total repaid minus borrowed

Total interest over a loan with equal payments.

  1. Multiply the payment by the number of payments.
  2. Take away the amount borrowed. What remains is the interest.
worked example

Example: You borrow $6,000 and repay it with 24 monthly payments of $275. How much interest do you pay in total?

  1. 24 × $275 = $6,600.
  2. $6,600 − $6,000 = $600.

Answer: $600

Tips by skill

  • TipThis month's interest: Turn the monthly rate into a decimal (1.5% is 0.015), then multiply it by the balance.
  • TipBalance after one payment: Interest first. Only the rest of the payment reduces what you owe.
  • TipBalance after two payments: One month at a time: add interest on the current balance, then subtract the payment.
  • TipTotal interest over the loan: The payment times the number of payments, minus the amount borrowed.

Watch out for

  • Taking the whole payment off the principal. Part of it pays interest, so the balance falls by less than the payment.
  • Charging month 2's interest on the original balance instead of the smaller balance after month 1.
  • Giving the total repaid as the interest.
  • Moving the decimal one place too few: 0.75% is 0.0075, not 0.075.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

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