a college student is buying a new car which cost $16 500 plus 8 sales tax. the t
ID: 1232133 • Letter: A
Question
a college student is buying a new car which cost $16 500 plus 8 sales tax. the title, license, and registration fees are $650. the dealer offers her a financing program that starts with a small monthly payment, and the payment will gradually increase. The dealer offers to finance 80% of the car's price for 48 months at a nominal interest rate of 9% per year, compounded monthly. the first payment is $300 and each successive payment will increase be a constant dollar amount X.a)How much is the constant amount X?
b)How much is the 48th payment?
Explanation / Answer
total cost = 16500 + (16500*8%) + 650
= 18470
finance amount = 80% of total = 80% * 18470 = 14776
number of payments = 48
interest per month = (1+9%)^(1/12) - 1 = 0.77273%
this can be solved in excel
installment increases every month by a constant amount and sum of all PVs must be equal to 14776
you get the constant x = 2.9489 dollars
and the 48th payment is 438.60
below is the excel table.
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installment increment
2.9489
Sum of PV
14,776.04
month
intallment
PV of installment
1
300.00
297.85
2
302.95
298.63
3
305.90
299.38
4
308.85
300.10
5
311.80
300.80
6
314.74
301.47
7
317.69
302.12
8
320.64
302.74
9
323.59
303.34
10
326.54
303.91
11
329.49
304.46
12
332.44
304.99
13
335.39
305.49
14
338.34
305.97
15
341.28
306.43
16
344.23
306.87
17
347.18
307.28
18
350.13
307.67
19
353.08
308.05
20
356.03
308.40
21
358.98
308.72
22
361.93
309.03
23
364.88
309.32
24
367.82
309.59
25
370.77
309.84
26
373.72
310.07
27
376.67
310.28
28
379.62
310.47
29
382.57
310.64
30
385.52
310.80
31
388.47
310.93
32
391.42
311.05
33
394.36
311.15
34
397.31
311.24
35
400.26
311.30
36
403.21
311.35
37
406.16
311.39
38
409.11
311.40
39
412.06
311.40
40
415.01
311.39
41
417.96
311.36
42
420.90
311.31
43
423.85
311.25
44
426.80
311.17
45
429.75
311.08
46
432.70
310.97
47
435.65
310.85
48
438.60
310.71
installment increment
2.9489
Sum of PV
14,776.04
month
intallment
PV of installment
1
300.00
297.85
2
302.95
298.63
3
305.90
299.38
4
308.85
300.10
5
311.80
300.80
6
314.74
301.47
7
317.69
302.12
8
320.64
302.74
9
323.59
303.34
10
326.54
303.91
11
329.49
304.46
12
332.44
304.99
13
335.39
305.49
14
338.34
305.97
15
341.28
306.43
16
344.23
306.87
17
347.18
307.28
18
350.13
307.67
19
353.08
308.05
20
356.03
308.40
21
358.98
308.72
22
361.93
309.03
23
364.88
309.32
24
367.82
309.59
25
370.77
309.84
26
373.72
310.07
27
376.67
310.28
28
379.62
310.47
29
382.57
310.64
30
385.52
310.80
31
388.47
310.93
32
391.42
311.05
33
394.36
311.15
34
397.31
311.24
35
400.26
311.30
36
403.21
311.35
37
406.16
311.39
38
409.11
311.40
39
412.06
311.40
40
415.01
311.39
41
417.96
311.36
42
420.90
311.31
43
423.85
311.25
44
426.80
311.17
45
429.75
311.08
46
432.70
310.97
47
435.65
310.85
48
438.60
310.71
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