amortization

Also called: amortisation, amortization schedule, loan amortization

Repaying a loan in installments, each covering that month’s interest first and repaying principal with the rest: B(t+1) = B(t) × (1 + r) − payment. With equal payments the interest part shrinks and the principal part grows.

An amortizing loan is repaid in installments. Each month the balance grows by the interest and shrinks by the payment:

$B_{t+1} = B_t \times (1 + r) - \text{payment}$

The payment covers that month’s interest first; the rest repays principal. With equal payments, interest is always r × a smaller balance, so later payments repay more of the loan. The table of these splits is the amortization schedule.

The price of the loan is everything paid minus what was borrowed: n × payment − principal. A payment at or below the monthly interest never clears the debt, which is the minimum-payment trap on credit cards.

The real rate of a loan is its internal rate: the r at which the discounted payments equal the money actually received, found with RATE or IRR in a spreadsheet. A flat fee charged on the original amount, or an upfront fee, pushes that rate well above the advertised one.

Example

60,000 UAH at 2% a month, six payments of 10,711.55:

Month 1: interest 1,200, principal 9,511.55, balance 50,488.45.
Month 6: interest 210.03, principal 10,501.52, balance 0.
Price of the loan: 6 × 10,711.55 − 60,000 = 4,269.30 UAH.

Common mistakes

Assuming the interest part is constant. It shrinks with the balance.
Paying only the interest. The balance never moves.
Trusting a flat monthly fee as the rate. 1.5% a month on the original amount repaid in four parts is about 28% a year, not 18%.
Forgetting upfront fees. You receive less but repay the same, so the real rate rises.

Learn it in the course

Loans and amortization · How a payment splits into interest and principal, months to repay, a flat fee against interest on the balance, and the real annual cost of a loan as its internal rate.