Archive / Mutual Fund Distributors / Investment Landscape

nism-series-va-effective-annual-rate-credit-card-calculation[ MUTUAL FUND DISTRIBUTORS ]

A commercial credit card charges an interest financing rate of 3.50% per month on revolving unpaid balances. What is the true Effective Annual Rate (EAR) incurred by the cardholder per annum?

[ A ]42.00% p.a. (Nominal APR = 3.5% * 12)

[ B ]35.00% p.a.

[ C ]55.50% p.a.

[ D ]51.11% p.a. [ (1 + r_monthly)^12 - 1 = (1 + 0.035)^12 - 1 ][ CORRECT ]

Takeaway

Option D is correct: 51.11% p.a. [ (1 + r_monthly)^12 - 1 = (1 + 0.035)^12 - 1 ]

Derivation

Monthly rate = 3.50% = 0.035. Applying the effective annual rate formula for 12 monthly compounding periods: EAR = (1.035)^12 − 1. Raising 1.035 to the 12th power gives approximately 1.511068, so EAR = 51.11% p.a. Compare this to what the card issuer typically advertises — the nominal APR of 3.5% × 12 = 42.00% — and the 9.11-percentage-point gap is purely the effect of monthly compounding on a revolving balance. This is the exact mechanism credit card issuers rely on: quoting a modest-sounding monthly rate obscures a much larger true annual cost, and cardholders who only ever see '3.5% a month' in the statement routinely underestimate what carrying a balance actually costs over a year.

Why the others fail

A — 42.00% p.a. (Nominal APR = 3.5% * 12)

42.00% is the simple nominal APR (3.5% × 12), which ignores that interest compounds monthly on the growing balance — the true annualized cost is higher.

B — 35.00% p.a.

35.00% comes from an arbitrary multiplier and does not correspond to either the nominal APR calculation or the compounded effective annual rate.

C — 55.50% p.a.

55.50% overstates the compounding effect — the correct twelve-period compounding of a 3.5% monthly rate yields 51.11%, not this higher figure.