Question

In: Finance

Assume that you have a balance of $3000 on your MasterCard and that you make no...

Assume that you have a balance of $3000 on your MasterCard and that you make no more charges. Assume that MasterCard charges 12% APR and that each month you make only the minimum payment of 5% of the balance.

Find how many months it will take to bring the remaining balance down to $400. (Round your answer to the nearest whole number.)

Please do NOT use Excel

Solutions

Expert Solution

ANSWER: 48 Months

Interest in each month = opening balance * (APR / 12)

We divide by 12 as we are calculating interest for 1 month

= 3000*12/100*1/12=30

Payment in each month = (opening balance + interest for the month) * 5%

closing balance of each month = opening balance + interest - payment

For 1st Month=3000*12/100*1/12=30

=3000+30-5/100

=2878.50

It goes till 48 months to reach the balance down to 400.

48th Month= 429.05*12/100*1/12

=429.05+4.29-21.67

=411.68

Months Opening Bal Interest Total Mini.Payment Closing Balance
1 3,000.00                             30.00           3,030.00                151.50                        2,878.50
2 2,878.50                             28.79           2,907.29                145.36                        2,761.92
3 2,761.92                             27.62           2,789.54                139.48                        2,650.06
4 2,650.06                             26.50           2,676.56                133.83                        2,542.74
5 2,542.74                             25.43           2,568.16                128.41                        2,439.75
6 2,439.75                             24.40           2,464.15                123.21                        2,340.94
7 2,340.94                             23.41           2,364.35                118.22                        2,246.14
8 2,246.14                             22.46           2,268.60                113.43                        2,155.17
9 2,155.17                             21.55           2,176.72                108.84                        2,067.88
10 2,067.88                             20.68           2,088.56                104.43                        1,984.13
11 1,984.13                             19.84           2,003.98                100.20                        1,903.78
12 1,903.78                             19.04           1,922.81                   96.14                        1,826.67
13 1,826.68                             18.27           1,844.94                   92.25                        1,752.70
14 1,752.70                             17.53           1,770.22                   88.51                        1,681.71
15 1,681.71                             16.82           1,698.53                   84.93                        1,613.60
16 1,613.60                             16.14           1,629.74                   81.49                        1,548.25
17 1,548.25                             15.48           1,563.73                   78.19                        1,485.55
18 1,485.55                             14.86           1,500.40                   75.02                        1,425.38
19 1,425.38                             14.25           1,439.64                   71.98                        1,367.65
20 1,367.66                             13.68           1,381.33                   69.07                        1,312.26
21 1,312.27                             13.12           1,325.39                   66.27                        1,259.12
22 1,259.12                             12.59           1,271.71                   63.59                        1,208.12
23 1,208.12                             12.08           1,220.21                   61.01                        1,159.19
24 1,159.20                             11.59           1,170.79                   58.54                        1,112.25
25 1,112.25                             11.12           1,123.37                   56.17                        1,067.20
26 1,067.20                             10.67           1,077.87                   53.89                        1,023.98
27 1,023.98                             10.24           1,034.22                   51.71                            982.51
28      982.51                                9.83               992.33                   49.62                            942.72
29      942.72                                9.43               952.14                   47.61                            904.54
30      904.54                                9.05               913.58                   45.68                            867.90
31      867.90                                8.68               876.58                   43.83                            832.75
32      832.75                                8.33               841.08                   42.05                            799.03
33      799.03                                7.99               807.02                   40.35                            766.67
34      766.67                                7.67               774.33                   38.72                            735.62
35      735.62                            

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