Which rate is really higher?
A quoted rate charged monthly costs more than the same rate charged once a year, because interest is charged on earlier interest. The effective annual rate puts every offer on the same footing.
- Offer 1Best
- 12.55%
- 12.00% · Quarterly
- Offer 2
- 12.57%
- 11.90% · Monthly
- Offer 3
- 12.60%
- 12.60% · Yearly
Offer 1 is the best: 12.55% a year once compounding is counted.
- Quoted rate
- Effective annual rate
Lenders must also disclose the APR: the effective rate including fees, so loans can be compared.
How it works
The same sum with your numbers, step by step.
Rate per period: the quoted rate divided by the times a year interest is charged
Offer 1: 12% ÷ 4 = 0.03 Offer 2: 11.9% ÷ 12 = 0.009917 Offer 3: 12.6% ÷ 1 = 0.126
Add 1 and raise it to the number of periods in a year
Offer 1: (1 + 0.03)⁴ = 1.125509 Offer 2: (1 + 0.009917)¹² = 1.12571 Offer 3: (1 + 0.126)¹ = 1.126
Take away 1: the effective annual rate
Offer 1: 1.125509 − 1 = 0.125509 = 12.55% Offer 2: 1.12571 − 1 = 0.12571 = 12.57% Offer 3: 1.126 − 1 = 0.126 = 12.60%
Where this appears in the CME
The effective annual rate is in CME-1A, chapter 9 (Other financial products), section 2.2. The workbook's example: 12% a year charged quarterly is 12.55% a year.
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