Banks quote annual rates but compound more often, and the label understates the reality. If a rate of 12% is compounded monthly, you earn (or owe) 1% per month, and twelve monthly compoundings beat one annual one:
FV after 1 year = PV × (1 + 0.12/12)^12 = PV × 1.1268
How do you calculate EAR and compare it with APR?
Now the general machinery. Let m be the number of compounding periods per year and APR the quoted annual rate. APR also goes by nominal quoted rate or stated rate, an unlucky clash with the "nominal vs real" distinction you'll meet later. They're different ideas. In symbols:
- Periodic rate =
APR / m - FV over n years =
PV × (1 + APR/m)^(m·n) - Effective Annual Rate:
EAR = (1 + APR/m)^m − 1
EAR is the true one-year growth rate, and it's the only number you can compare two instruments on. Here's the same 12% APR at different frequencies:
| Compounding | m | EAR |
|---|---|---|
| Annual | 1 | 12.0000% |
| Semiannual | 2 | 12.3600% |
| Quarterly | 4 | 12.5509% |
| Monthly | 12 | 12.6825% |
| Daily | 365 | 12.7475% |
| Continuous | → ∞ | 12.7497% |
Two lessons. Frequency matters, because monthly against annual opens a 0.68-point gap on the same label. And the effect saturates fast, so going from daily to continuous adds almost nothing. Continuous compounding, FV = PV·e^(r·t), is the mathematical limit. ₹1,00,000 at 12% continuous for a year gives ₹1,12,749.69. You'll meet it in option pricing and academic papers. For analyst work, know it exists and move on.
The comparison rule: convert everything to EAR, then compare. Quoted rates are marketing. EAR is economics. A deposit quoting 11.9% compounded monthly (EAR 12.57%) beats one quoting 12.0% quarterly (EAR 12.55%), and both beat 12.1% semiannual (EAR 12.47%). So the lowest label pays the most. You can't see that without converting.
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Which India traps hide the true cost of a loan?
Two India-specific traps deserve a permanent place in your head.
Trap 1: the monthly-quoted credit-card rate. Indian card issuers quote ~3.0 to 3.6% per month. 3.5% a month sounds small. It's an APR of 42% and an EAR of 1.035^12 − 1 = 51.1%. A US card quoting "24% APR" compounded monthly is an EAR of 26.8%. Neither label tells you what the card costs. Only the EAR does.
Trap 2: the flat-rate loan. It's common in Indian vehicle and personal lending, quoted as "8% flat." Your lender computes interest on the original principal for the whole tenor, as if your EMIs weren't steadily paying it down. Borrow ₹1,00,000 for 2 years at 8% flat. Interest is 1,00,000 × 8% × 2 = ₹16,000, so you repay ₹1,16,000 in 24 EMIs of ₹4,833.33. On a reducing-balance basis, which is the true cost of the money you actually had the use of, the implied monthly rate is 1.223%, an APR of ~14.7% and an EAR of 15.7%. "8% flat" is a ~15.7% loan. You'll prove this yourself with IRR in the practice set. As a rule of thumb, a flat rate is about half the true reducing rate, and for the exact answer you solve the IRR. RBI's Key Facts Statement rules now force lenders to disclose an all-in APR. Read that line and ignore the headline. In the US, the equivalent is the Truth in Lending Act's APR against the advertised teaser. And the same defense works everywhere: convert to effective, then compare.
Worked example: a bank FD quoting 7.2% compounded quarterly
Deposit-side example (India). Take a bank FD quoting 7.2% compounded quarterly. Its EAR is (1 + 0.072/4)^4 − 1 = 7.40%. Indian G-secs pay semiannual coupons, so a "7.0%" G-sec yield convention is an EAR of 1.035^2 − 1 = 7.12%. They're small gaps, you might say. You're training to notice small gaps, though, because in valuation they compound for decades.