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 |