Question 321982
Balance in credit card account = $6100.00
Annual Interest Rate is 12%


Card to be payed off in 4 years without any additional purchases to be made.


Essentially this is like a loan that you're paying off in 4 years.


Interest Rate and payments are monthly so we need to make some adjustments.


Number of Periods of the loan is 4 * 12 = 48.


Interest rate per period is 12% / 12 = 1%.


There is an annuity formula to use that I will give you later on.


In the meantime I will use a financial calculator to solve this problem.


The financial calculator tells me that the monthly payments need to be $160.6363961.


You can round that to the nearest penny but I'll leave it as is until I finish with all the calculations.


The total payment made over the 4 year period will be 48 * $160.6363961 = $7,710.547013.


Since the balance was $6,100, then the total interest paid was $7,710.547013 minus $6,100 = $1,610.547013.


The Monthly Details of this analysis are shown below:


<pre>
Sum of Principal = $6,100.00
Sum of Interest  = $1,610.55
$1,610.55
TP = Time Period	
PP = Payment Principal = Amount of Principal in each Payment.
PI = Payment Interest  = Amount of Interest in each Payment.
PT = Payment Total     = Amount of Principal + Interest in each Payment.
RB = Remaining Balance = Remaining Balance in Account after each Payment
                         is made.
TP      PP      PI      TP      RB		
0                               $6,100.00
1	$99.64	$61.00	$160.64	$6,000.36			
2	$100.63	$60.00	$160.64	$5,899.73			
3	$101.64	$59.00	$160.64	$5,798.09			
4	$102.66	$57.98	$160.64	$5,695.44			
5	$103.68	$56.95	$160.64	$5,591.75			
6	$104.72	$55.92	$160.64	$5,487.04			
7	$105.77	$54.87	$160.64	$5,381.27			
8	$106.82	$53.81	$160.64	$5,274.45			
9	$107.89	$52.74	$160.64	$5,166.55			
10	$108.97	$51.67	$160.64	$5,057.58			
11	$110.06	$50.58	$160.64	$4,947.52			
12	$111.16	$49.48	$160.64	$4,836.36			
13	$112.27	$48.36	$160.64	$4,724.09			
14	$113.40	$47.24	$160.64	$4,610.69			
15	$114.53	$46.11	$160.64	$4,496.16			
16	$115.67	$44.96	$160.64	$4,380.49			
17	$116.83	$43.80	$160.64	$4,263.66			
18	$118.00	$42.64	$160.64	$4,145.66			
19	$119.18	$41.46	$160.64	$4,026.48			
20	$120.37	$40.26	$160.64	$3,906.11			
21	$121.58	$39.06	$160.64	$3,784.53			
22	$122.79	$37.85	$160.64	$3,661.74			
23	$124.02	$36.62	$160.64	$3,537.72			
24	$125.26	$35.38	$160.64	$3,412.46			
25	$126.51	$34.12	$160.64	$3,285.95			
26	$127.78	$32.86	$160.64	$3,158.17			
27	$129.05	$31.58	$160.64	$3,029.12			
28	$130.35	$30.29	$160.64	$2,898.77			
29	$131.65	$28.99	$160.64	$2,767.12			
30	$132.97	$27.67	$160.64	$2,634.16			
31	$134.29	$26.34	$160.64	$2,499.86			
32	$135.64	$25.00	$160.64	$2,364.23			
33	$136.99	$23.64	$160.64	$2,227.23			
34	$138.36	$22.27	$160.64	$2,088.87			
35	$139.75	$20.89	$160.64	$1,949.12			
36	$141.15	$19.49	$160.64	$1,807.98			
37	$142.56	$18.08	$160.64	$1,665.42			
38	$143.98	$16.65	$160.64	$1,521.44			
39	$145.42	$15.21	$160.64	$1,376.01			
40	$146.88	$13.76	$160.64	$1,229.14			
41	$148.35	$12.29	$160.64	$1,080.79			
42	$149.83	$10.81	$160.64	$930.96			
43	$151.33	$9.31	$160.64	$779.64			
44	$152.84	$7.80	$160.64	$626.80			
45	$154.37	$6.27	$160.64	$472.43			
46	$155.91	$4.72	$160.64	$316.52			
47	$157.47	$3.17	$160.64	$159.05			
48	$159.05	$1.59	$160.64	$0.00			
</pre>


The formula for Payment of a Present Amount is the formula you use to solve this type of problem.


That formula is shown below:


PAYMENT FOR A PRESENT VALUE


{{{ PMT(PV) = (PV / ((((1 - (1 / ((1+i)^n))))/i))) }}}


PMT = Payment per Time Period	
PV = Present Value
i = Interest Rate per Time Period
n = Number of Time Periods


PV = $6,100
i = .12 / 12 = .01
n = 4 * 12 = 48


Plug these values into the equation and solve.


Equation becomes:



{{{ PMT(6100) = (6100 / ((((1 - (1 / ((1.01)^48))))/.01))) }}}


After plugging the value into this equation, you should come up with:


PMT(6100) = 160.6363961