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Credit Card Installment Calculator · Monthly Fee → Real APR · Newton IRR

Credit card installments often advertise a 0.6%/mo fee, implying ~7% a year — but the true APR is ~13.5%. This tool solves IRR via Newton's method to compute the real APR, plus monthly payment, total fee, and nominal-vs-real comparison. Supports monthly fee rate or total fee rate input.

Overview

Credit card installments advertise "0.6% monthly fee" — but since you pay down principal each month, the real APR is ~13.5%, nearly 2× the quoted rate. This is the classic IRR problem. Tool uses Newton's method (100 iter, 1e-10 tol) to output monthly payment, total fee, nominal APR, real APR, and EAR. Supports both monthly and total fee rate inputs. All local.

How to use

  1. Enter principal and term (3-60 months).
  2. Choose fee input mode (monthly rate or total rate).
  3. See monthly payment, total fee, nominal APR, real APR, and EAR live.
  4. Compare real-to-nominal ratio (typically 1.7×-2.0×) to decide.

Formula

monthly = principal/n + principal · monthlyFeeRate
nominalApr = monthlyFeeRate · 12
realApr via Newton IRR: Σ monthly/(1+r)^k = principal → r_month
EAR = (1 + r_month)^12 − 1
totalMode: monthlyFeeRate = totalFeeRate / n

Common scenarios

10k · 12mo · 0.6%/mo

monthly 893.33, total fee 720, nominal 7.2%, real APR ≈ 13.03%, ratio 1.81×.

30k · 24mo · 0.55%/mo

monthly 1415, fee 3960, real APR ≈ 12.25%, ratio 1.86×.

5k · 3mo · 2.4% total

→ 0.8%/mo, monthly 1706.67, real APR ≈ 14.13%, ratio 1.47×.

FAQ

Why is real APR nearly 2× the nominal?

Average outstanding principal is ≈ 50% of loan, but fee is charged on full principal. So real APR ≈ nominal × 2n/(n+1). Ratio approaches 2× as n grows.

Is installment better than a personal loan?

Usually no — personal loans (LPR-based, 3.6-7.2%) beat installments (12-18%). Exceptions are small-amount short-term, or zero-fee promos.

Why isn't the monthly fee rate ad regulated?

PBoC 2021 requires APR disclosure for loans, but credit installments sit in a gray zone. Shanghai Financial Court (2022) ruled they must disclose real APR via IRR. Enforcement uneven.

Can I save fees by prepaying?

Usually no — most banks keep full fee even if you prepay. Few banks refund with penalty. Installment is largely irreversible — compute real cost first.

Is my data uploaded?

No — the entire IRR calculation runs locally in your browser.

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