Question
In: Finance
The price of a car you are interested in buying is $93.65k. You negotiate a 6-year...
The price of a car you are interested in buying is $93.65k. You negotiate a 6-year loan, with no money down and no monthly payments during the first year. After the first year, you will pay $1.26k per month for the following 5 years, with a balloon payment at the end to cover the remaining principal on the loan. The annual percentage rate (APR) on the loan with monthly compounding is 5%. What will be the amount of the balloon payment 6 years from now?
Note: The term “k” is used to represent thousands (× $1,000).
Required: Suppose the loan has initially been paid in full (without a balance due at maturity), the amount would have totaled $37k. Calculate the absolute percentage difference between the fully amortized loan and the balloon payment.
Solutions
Expert Solution
Calculation of Payment to be made under Balloon Payment System
|
Month End |
Beginning Balance |
Ending Balance before Payment |
Paid |
Balance |
|
0-12 |
$ 93,650.00 |
$ 98,441.31 |
$ - |
$ 98,441.31 |
|
13 |
$ 98,441.31 |
$ 98,851.48 |
$ 1,260.00 |
$ 97,591.48 |
|
14 |
$ 97,591.48 |
$ 97,998.12 |
$ 1,260.00 |
$ 96,738.12 |
|
15 |
$ 96,738.12 |
$ 97,141.19 |
$ 1,260.00 |
$ 95,881.19 |
|
16 |
$ 95,881.19 |
$ 96,280.70 |
$ 1,260.00 |
$ 95,020.70 |
|
17 |
$ 95,020.70 |
$ 95,416.62 |
$ 1,260.00 |
$ 94,156.62 |
|
18 |
$ 94,156.62 |
$ 94,548.93 |
$ 1,260.00 |
$ 93,288.93 |
|
19 |
$ 93,288.93 |
$ 93,677.64 |
$ 1,260.00 |
$ 92,417.64 |
|
20 |
$ 92,417.64 |
$ 92,802.71 |
$ 1,260.00 |
$ 91,542.71 |
|
21 |
$ 91,542.71 |
$ 91,924.14 |
$ 1,260.00 |
$ 90,664.14 |
|
22 |
$ 90,664.14 |
$ 91,041.91 |
$ 1,260.00 |
$ 89,781.91 |
|
23 |
$ 89,781.91 |
$ 90,156.00 |
$ 1,260.00 |
$ 88,896.00 |
|
24 |
$ 88,896.00 |
$ 89,266.40 |
$ 1,260.00 |
$ 88,006.40 |
|
25 |
$ 88,006.40 |
$ 88,373.09 |
$ 1,260.00 |
$ 87,113.09 |
|
26 |
$ 87,113.09 |
$ 87,476.06 |
$ 1,260.00 |
$ 86,216.06 |
|
27 |
$ 86,216.06 |
$ 86,575.30 |
$ 1,260.00 |
$ 85,315.30 |
|
28 |
$ 85,315.30 |
$ 85,670.78 |
$ 1,260.00 |
$ 84,410.78 |
|
29 |
$ 84,410.78 |
$ 84,762.49 |
$ 1,260.00 |
$ 83,502.49 |
|
30 |
$ 83,502.49 |
$ 83,850.42 |
$ 1,260.00 |
$ 82,590.42 |
|
31 |
$ 82,590.42 |
$ 82,934.54 |
$ 1,260.00 |
$ 81,674.54 |
|
32 |
$ 81,674.54 |
$ 82,014.85 |
$ 1,260.00 |
$ 80,754.85 |
|
33 |
$ 80,754.85 |
$ 81,091.33 |
$ 1,260.00 |
$ 79,831.33 |
|
34 |
$ 79,831.33 |
$ 80,163.96 |
$ 1,260.00 |
$ 78,903.96 |
|
35 |
$ 78,903.96 |
$ 79,232.73 |
$ 1,260.00 |
$ 77,972.73 |
|
36 |
$ 77,972.73 |
$ 78,297.61 |
$ 1,260.00 |
$ 77,037.61 |
|
37 |
$ 77,037.61 |
$ 77,358.60 |
$ 1,260.00 |
$ 76,098.60 |
|
38 |
$ 76,098.60 |
$ 76,415.68 |
$ 1,260.00 |
$ 75,155.68 |
|
39 |
$ 75,155.68 |
$ 75,468.83 |
$ 1,260.00 |
$ 74,208.83 |
|
40 |
$ 74,208.83 |
$ 74,518.03 |
$ 1,260.00 |
$ 73,258.03 |
|
41 |
$ 73,258.03 |
$ 73,563.28 |
$ 1,260.00 |
$ 72,303.28 |
|
42 |
$ 72,303.28 |
$ 72,604.54 |
$ 1,260.00 |
$ 71,344.54 |
|
43 |
$ 71,344.54 |
$ 71,641.81 |
$ 1,260.00 |
$ 70,381.81 |
|
44 |
$ 70,381.81 |
$ 70,675.07 |
$ 1,260.00 |
$ 69,415.07 |
|
45 |
$ 69,415.07 |
$ 69,704.30 |
$ 1,260.00 |
$ 68,444.30 |
|
46 |
$ 68,444.30 |
$ 68,729.48 |
$ 1,260.00 |
$ 67,469.48 |
|
47 |
$ 67,469.48 |
$ 67,750.60 |
$ 1,260.00 |
$ 66,490.60 |
|
48 |
$ 66,490.60 |
$ 66,767.65 |
$ 1,260.00 |
$ 65,507.65 |
|
49 |
$ 65,507.65 |
$ 65,780.60 |
$ 1,260.00 |
$ 64,520.60 |
|
50 |
$ 64,520.60 |
$ 64,789.43 |
$ 1,260.00 |
$ 63,529.43 |
|
51 |
$ 63,529.43 |
$ 63,794.14 |
$ 1,260.00 |
$ 62,534.14 |
|
52 |
$ 62,534.14 |
$ 62,794.70 |
$ 1,260.00 |
$ 61,534.70 |
|
53 |
$ 61,534.70 |
$ 61,791.09 |
$ 1,260.00 |
$ 60,531.09 |
|
54 |
$ 60,531.09 |
$ 60,783.30 |
$ 1,260.00 |
$ 59,523.30 |
|
55 |
$ 59,523.30 |
$ 59,771.32 |
$ 1,260.00 |
$ 58,511.32 |
|
56 |
$ 58,511.32 |
$ 58,755.11 |
$ 1,260.00 |
$ 57,495.11 |
|
57 |
$ 57,495.11 |
$ 57,734.68 |
$ 1,260.00 |
$ 56,474.68 |
|
58 |
$ 56,474.68 |
$ 56,709.99 |
$ 1,260.00 |
$ 55,449.99 |
|
59 |
$ 55,449.99 |
$ 55,681.03 |
$ 1,260.00 |
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