DebtSmart.com Sunday, January 24, 2021

Household Math: Minimum Payment Balance

by Scott Bilker
Scott Bilker Scott Bilker is the founder of DebtSmart.com and author of the best-selling books, Talk Your Way Out of Credit Card DebtCredit Card and Debt Management, and How to be more Credit Card and Debt Smart. Receive the 5-Year Loan Spreadsheet when you subscribe to his email newsletter.

Joan owes Visa $2,500. The credit card company has an interest rate of 19.6% APR. The company requires a minimum payment of 2% of the unpaid balance, rounded to the nearest dollar. Joan makes no additional purchases with this credit card and makes only one minimum payment monthly.

How long will it take her to pay off $500 on the $2,500 balance? (16 months, 36 months, 56 months, or 76 months)

 

Answer: 56 months

Explanation:

This is a straightforward problem that requires many calculations.

The starting balance is $2,500.

The interest rate (APR) is 19.6%. Therefore, the monthly rate is 19.6%/12 = 1.6333%

Step #1: Compute the interest for the first month.

Interest = $2,500 x 1.6333% = $40.83

Step #2: Compute the minimum payment.

Minimum Payment = ($2,500 + $40.83) x 2% = $50.82

Round to nearest dollar.

Minimum Payment = $51.00

Step 3: Calculate balance after interest and minimum payment.

Balance in month #1 = $2,500 + $40.83 – $51.00 = $2,489.53

Continue: Repeat those steps for each month until balance is less than or equal to $2,000.00.

Month

Interest

Payment

Balance

0

2,500.00

1

40.83

51.00

2,489.83

2

40.67

51.00

2,479.50

3

40.50

50.00

2,470.00

4

40.34

50.00

2,460.34

5

40.19

50.00

2,450.53

6

40.03

50.00

2,440.56

7

39.86

50.00

2,430.42

8

39.70

49.00

2,421.12

9

39.54

49.00

2,411.66

10

39.39

49.00

2,402.05

11

39.23

49.00

2,392.28

12

39.07

49.00

2,382.35

13

38.91

48.00

2,373.26

14

38.76

48.00

2,364.02

15

38.61

48.00

2,354.63

16

38.46

48.00

2,345.09

17

38.30

48.00

2,335.39

18

38.14

47.00

2,326.53

19

38.00

47.00

2,317.53

20

37.85

47.00

2,308.38

21

37.70

47.00

2,299.08

22

37.55

47.00

2,289.63

23

37.40

47.00

2,280.03

24

37.24

46.00

2,271.27

25

37.10

46.00

2,262.37

26

36.95

46.00

2,253.32

27

36.80

46.00

2,244.12

28

36.65

46.00

2,234.77

29

36.50

45.00

2,226.27

30

36.36

45.00

2,217.63

31

36.22

45.00

2,208.85

32

36.08

45.00

2,199.93

33

35.93

45.00

2,190.86

34

35.78

45.00

2,181.64

35

35.63

44.00

2,173.27

36

35.50

44.00

2,164.77

37

35.36

44.00

2,156.13

38

35.22

44.00

2,147.35

39

35.07

44.00

2,138.42

40

34.93

43.00

2,130.35

41

34.80

43.00

2,122.15

42

34.66

43.00

2,113.81

43

34.53

43.00

2,105.34

44

34.39

43.00

2,096.73

45

34.25

43.00

2,087.98

46

34.10

42.00

2,080.08

47

33.97

42.00

2,072.05

48

33.84

42.00

2,063.89

49

33.71

42.00

2,055.60

50

33.57

42.00

2,047.17

51

33.44

42.00

2,038.61

52

33.30

41.00

2,030.91

53

33.17

41.00

2,023.08

54

33.04

41.00

2,015.12

55

32.91

41.00

2,007.03

56

32.78

41.00

1,998.81