Type of calculation: How many fixed monthly payments it takes to clear a revolving credit-card balance, and the interest cost along the way.
Watch out: If your payment is smaller than the monthly interest, the balance grows instead of shrinking and the card is never paid off.
The formula:
First turn the APR into a monthly rate, then solve for the number of payments:
- i = APR / 100 / 12 (monthly rate)
- n = −ln(1 − i × B / PMT) / ln(1 + i) (number of payments)
Given: B = $
3000, APR =
20%, payment = $
150
i =
20 / 100 / 12 ≈
0.016667
Monthly interest = B × i = $
3000 ×
0.016667 = $
50 (your payment of $
150 is larger, so the balance goes down)
n = −ln(1 −
0.016667 × $
3000 / $
150) / ln(1 +
0.016667)
n =
−ln(0.666667) / ln(1.016667)B / PMT = $3000 / $150 ≈ 24.53 payments
A fraction of a payment is not possible, so the card is cleared by
24 full payments plus a smaller final payment —
25 months in total.
Balance left after the full payments ≈ $78.51, so the final payment is $78.51 × 1.016667 ≈ $79.82
Total paid = PMT ×
24 + final payment =
$
150 ×
24
+ $79.82 ≈ $
3679.82
Total interest = Total paid − B = $
3679.82 − $
3000 ≈ $
679.82