Archive / Investment Adviser (Level 1) / Debt Management and Loans

nism-series-xa-effective-annual-rate-credit-card-calculation[ INVESTMENT ADVISER (LEVEL 1) ]

A leading credit card issuer in India charges a monthly financing rate of 3.60% on revolving unpaid balances. What is the true Effective Annual Rate (EAR) incurred by the cardholder per annum?

[ A ]43.20% p.a.

[ B ]52.88% p.a.[ CORRECT ]

[ C ]55.45% p.a.

[ D ]36.00% p.a.

Takeaway

Monthly compounding increases the nominal 43.20% APR to an Effective Annual Rate of 52.88% p.a.

Derivation

Monthly interest rate r_m = 3.60% = 0.036, compounded over m = 12 periods a year. EAR = (1 + 0.036)^12 − 1 = (1.036)^12 − 1. Raising 1.036 to the 12th power gives approximately 1.5288, so EAR = 52.88% p.a. The bank's advertised figure, the nominal APR of 3.6% × 12 = 43.20%, understates the true annual cost by nearly 9.7 percentage points because it treats each month's interest as if it never compounds on top of prior months' unpaid interest. This gap between quoted monthly rate and compounded annual reality is the standard trap in credit card and revolving-loan disclosures, and this exact calculation recurs across NISM exams with different monthly rates.

Why the others fail

A — 43.20% p.a.

Represents the simple nominal Annual Percentage Rate (3.6% × 12), which does not account for interest compounding on the balance month over month.

C — 55.45% p.a.

Overstates the compounding effect — raising 1.036 to the 12th power correctly yields 52.88%, not this higher figure obtained through a different method.

D — 36.00% p.a.

Multiplies the monthly rate by 10 rather than by the 12 compounding periods in a year, producing an arbitrary figure with no basis in the formula.