effective annual rate
Also called: EAR, effective annual interest rate
The yearly rate a monthly rate really adds up to once interest is charged on interest: (1 + monthly rate)¹² − 1.
Credit cards and many short loans quote a monthly rate. Multiplying it by twelve gives a simple yearly figure, but it understates the cost: interest left unpaid this month is itself charged interest next month. The effective annual rate includes that compounding.
The formula is (1 + r)¹² − 1, where r is the monthly rate as a decimal. At 2.5% a month it is (1.025)¹² − 1 ≈ 34.49% a year, not 30%. At 3.2% a month it is about 45.93%, not 38.4%. The higher the monthly rate, the bigger the gap.
The same idea works for savings: interest added monthly earns interest of its own. When fees are involved, the real annual rate of a loan goes further and includes them too; the effective annual rate is the part that comes from compounding alone.
Example
Sam's credit card charges 3.2% a month on a 52,800 UAH balance. Simple yearly: 12 × 3.2% = 38.4%. Effective: (1.032)¹² − 1 = 0.4593, or 45.93% a year. Paying only the month's interest, 1,689.60, keeps the balance at 52,800 and costs 20,275.20 a year.
Common mistakes
- Multiplying by twelve. It ignores interest on interest.
- Comparing a monthly rate with a yearly one. Convert first.
- Forgetting fees. For loans, compare the real annual rate, which includes them.