Question 321982: Your credit card has a balance of $6100.00 and an annula interest rate of 12%.
You decide to pay off the balance over 4 years. If there are no futher purchases charged to the card:
A) How much must you pay each month?
B) How much total interest will you pay?
THanks for the help!!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
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
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 = 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:
After plugging the value into this equation, you should come up with:
PMT(6100) = 160.6363961
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