Question

With only a​ part-time job and the need for a professional​ wardrobe, Rachel quickly maxed out her credit card the summer after graduation. With her first​ full-time paycheck in​ August, she vowed to pay ​$210 each month toward paying down her $7827 outstanding balance and not to use the card. The card has an annual interest rate of 18 percent. How long will it take Rachel to pay for her​ wardrobe? Should she shop for a new​ card? Why or why​ not?

Answer 1

Calculation By Excel Formula:

Steps to calculate:

-As yearly rate is 18% hence monthly would be 1.5% so fix it up with Formula.

-then calculate monthly interest.

- Deduct monthly interest from fixed monthly payment which is $210.

-Deduct monthly installment from principal amount to calculate further. As next interest amount will be calculated from remaining principal.

*** Working is below:

Rate of Interest p.a	18%
Principal Amount	7827
Rate p.m	0.015

Monthly Payment	Principal Paid	Interest Paid	Remaining Balance
210	92.595	117.405	7734.405
210	93.983925	116.0161	7640.421075
210	95.39368388	114.6063	7546.43715
210	96.80344275	113.1966	7451.043466
210	98.23434801	111.7657	7354.240023
210	99.68639965	110.3136	7256.005675
210	101.1599149	108.8401	7156.319276
210	102.6552109	107.3448	7055.159361
210	104.1726096	105.8274	6952.50415
210	105.7124378	104.2876	6848.33154
210	107.2750269	102.725	6742.619103
210	108.8607135	101.1393	6635.344076
210	110.4698389	99.53016	6526.483362
210	112.1027496	97.89725	6416.013523
210	113.7597971	96.2402	6303.910774
210	115.4413384	94.55866	6190.150977
210	117.1477353	92.85226	6074.709638
210	118.8793554	91.12064	5957.561903
210	120.6365715	89.36343	5838.682548
210	122.4197618	87.58024	5718.045976
210	124.2293104	85.77069	5595.626214
210	126.0656068	83.93439	5471.396904
210	127.9290464	82.07095	5345.331297
210	129.8200305	80.17997	5217.402251
210	131.7389662	78.26103	5087.58222
210	133.6862667	76.31373	4955.843254
210	135.6623512	74.33765	4822.156987
210	137.6676452	72.33235	4686.494636
210	139.7025805	70.29742	4548.826991
210	141.7675951	68.2324	4409.12441
210	143.8631338	66.13687	4267.356815
210	145.9896478	64.01035	4123.493681
210	148.1475948	61.85241	3977.504034
210	150.3374395	59.66256	3829.356439
210	152.5596534	57.44035	3679.018999
210	154.814715	55.18528	3526.459346
210	157.1031098	52.89689	3371.644631
210	159.4253305	50.57467	3214.541521
210	161.7818772	48.21812	3055.116191
210	164.1732571	45.82674	2893.334313
210	166.5999853	43.40001	2729.161056
210	169.0625842	40.93742	2562.561071
210	171.5615839	38.43842	2393.498487
210	174.0975227	35.90248	2221.936903
210	176.6709465	33.32905	2047.83938
210	179.2824093	30.71759	1871.168434
210	181.9324735	28.06753	1691.886024
210	184.6217096	25.37829	1509.953551
210	187.3506967	22.6493	1325.331841
210	190.1200224	19.87998	1137.981145
210	192.9302828	17.06972	947.8611222
210	195.7820832	14.21792	754.9308394
210	198.6760374	11.32396	559.1487562
210	201.6127687	8.387231	360.4727188
210	204.5929092	5.407091	158.8599501
210	207.6171007	2.382899	-45.73295909

It will take 55 Months to her to pay off the outstanding balance of the credit card. As you can see at 55th payment principal comes to NIL (which included reaming $158 added in last installment or can come up to 56th installment as well) and after that in started coming negative, hence the total months will be 55 to finish the installment.

Looking upon the current scenario, she is not in the position to carry on with their spending with the help of new credit card purchase. If she purchase a new credit card definitely she will end up with more credit. As mentioned, after august she is continued with her full time job which is going to help her monthly spending without credit card. Also, if full time job credits her account on timely basis then she will be able to cover up with the monthly credit card payment as well as good management of their expenses until she is not coming out of the debts. Hence, suggestion for her would be not to buy another credit card with this perspective.

But, as other kind of situations about her was not mentioned in the case i.e., weather she has dependent, about her monthly medical expenses if paid by employer, or in case of any contingency if he is having someone to help her out. Hence, we can't strongly suggest her to not to go for new credit card because of missing facts.