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Question 9: You have selected a $35,000 delivery van for your business. The auto dealership is...

Question 9:

You have selected a $35,000 delivery van for your business. The auto dealership is offering you two financing options. Loan #1 is a four-year loan, paid monthly, at 6.0%. Loan #2 is a five-year loan, paid monthly at 7.2%. How much more interest will Loan #2 cost over the time of the loan than Loan #1?

Solutions

Expert Solution

Loan 1

Monthly rate(M)= yearly rate/12= 0.50% Monthly payment= 821.98
Month Beginning balance (A) Monthly payment Interest = M*A Principal paid Ending balance
1 35000.00 821.98 175.00 646.98 34353.02
2 34353.02 821.98 171.77 650.21 33702.81
3 33702.81 821.98 168.51 653.46 33049.35
4 33049.35 821.98 165.25 656.73 32392.62
5 32392.62 821.98 161.96 660.01 31732.61
6 31732.61 821.98 158.66 663.31 31069.30
7 31069.30 821.98 155.35 666.63 30402.67
8 30402.67 821.98 152.01 669.96 29732.70
9 29732.70 821.98 148.66 673.31 29059.39
10 29059.39 821.98 145.30 676.68 28382.71
11 28382.71 821.98 141.91 680.06 27702.65
12 27702.65 821.98 138.51 683.46 27019.19
13 27019.19 821.98 135.10 686.88 26332.31
14 26332.31 821.98 131.66 690.31 25641.99
15 25641.99 821.98 128.21 693.77 24948.23
16 24948.23 821.98 124.74 697.23 24250.99
17 24250.99 821.98 121.25 700.72 23550.27
18 23550.27 821.98 117.75 704.22 22846.05
19 22846.05 821.98 114.23 707.75 22138.30
20 22138.30 821.98 110.69 711.28 21427.02
21 21427.02 821.98 107.14 714.84 20712.17
22 20712.17 821.98 103.56 718.42 19993.76
23 19993.76 821.98 99.97 722.01 19271.75
24 19271.75 821.98 96.36 725.62 18546.13
25 18546.13 821.98 92.73 729.25 17816.89
26 17816.89 821.98 89.08 732.89 17084.00
27 17084.00 821.98 85.42 736.56 16347.44
28 16347.44 821.98 81.74 740.24 15607.20
29 15607.20 821.98 78.04 743.94 14863.26
30 14863.26 821.98 74.32 747.66 14115.60
31 14115.60 821.98 70.58 751.40 13364.21
32 13364.21 821.98 66.82 755.15 12609.05
33 12609.05 821.98 63.05 758.93 11850.12
34 11850.12 821.98 59.25 762.73 11087.39
35 11087.39 821.98 55.44 766.54 10320.86
36 10320.86 821.98 51.60 770.37 9550.48
37 9550.48 821.98 47.75 774.22 8776.26
38 8776.26 821.98 43.88 778.09 7998.17
39 7998.17 821.98 39.99 781.99 7216.18
40 7216.18 821.98 36.08 785.90 6430.28
41 6430.28 821.98 32.15 789.82 5640.46
42 5640.46 821.98 28.20 793.77 4846.69
43 4846.69 821.98 24.23 797.74 4048.94
44 4048.94 821.98 20.24 801.73 3247.21
45 3247.21 821.98 16.24 805.74 2441.47
46 2441.47 821.98 12.21 809.77 1631.70
47 1631.70 821.98 8.16 813.82 817.89
48 817.89 821.98 4.09 817.89 0.00
Where
Interest paid = Beginning balance * Monthly interest rate
Principal = Monthly payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Month ending balance
total payment=Monthly payment*number of Month
=821.976*48
=39454.8479999999
Total interest paid= total payment-period 1 beginning balance
=39454.8479999999-35000
=4454.84799999999

Loan 2

Monthly rate(M)= yearly rate/12= 0.60% Monthly payment= 696.35
Month Beginning balance (A) Monthly payment Interest = M*A Principal paid Ending balance
1 35000.00 696.35 210.00 486.35 34513.65
2 34513.65 696.35 207.08 489.27 34024.38
3 34024.38 696.35 204.15 492.20 33532.18
4 33532.18 696.35 201.19 495.16 33037.02
5 33037.02 696.35 198.22 498.13 32538.90
6 32538.90 696.35 195.23 501.12 32037.78
7 32037.78 696.35 192.23 504.12 31533.66
8 31533.66 696.35 189.20 507.15 31026.51
9 31026.51 696.35 186.16 510.19 30516.32
10 30516.32 696.35 183.10 513.25 30003.07
11 30003.07 696.35 180.02 516.33 29486.74
12 29486.74 696.35 176.92 519.43 28967.31
13 28967.31 696.35 173.80 522.55 28444.76
14 28444.76 696.35 170.67 525.68 27919.08
15 27919.08 696.35 167.51 528.83 27390.25
16 27390.25 696.35 164.34 532.01 26858.24
17 26858.24 696.35 161.15 535.20 26323.04
18 26323.04 696.35 157.94 538.41 25784.63
19 25784.63 696.35 154.71 541.64 25242.99
20 25242.99 696.35 151.46 544.89 24698.10
21 24698.10 696.35 148.19 548.16 24149.94
22 24149.94 696.35 144.90 551.45 23598.49
23 23598.49 696.35 141.59 554.76 23043.73
24 23043.73 696.35 138.26 558.09 22485.64
25 22485.64 696.35 134.91 561.44 21924.21
26 21924.21 696.35 131.55 564.80 21359.40
27 21359.40 696.35 128.16 568.19 20791.21
28 20791.21 696.35 124.75 571.60 20219.61
29 20219.61 696.35 121.32 575.03 19644.57
30 19644.57 696.35 117.87 578.48 19066.09
31 19066.09 696.35 114.40 581.95 18484.14
32 18484.14 696.35 110.90 585.44 17898.70
33 17898.70 696.35 107.39 588.96 17309.74
34 17309.74 696.35 103.86 592.49 16717.25
35 16717.25 696.35 100.30 596.05 16121.20
36 16121.20 696.35 96.73 599.62 15521.58
37 15521.58 696.35 93.13 603.22 14918.36
38 14918.36 696.35 89.51 606.84 14311.52
39 14311.52 696.35 85.87 610.48 13701.04
40 13701.04 696.35 82.21 614.14 13086.90
41 13086.90 696.35 78.52 617.83 12469.07
42 12469.07 696.35 74.81 621.53 11847.53
43 11847.53 696.35 71.09 625.26 11222.27
44 11222.27 696.35 67.33 629.02 10593.25
45 10593.25 696.35 63.56 632.79 9960.46
46 9960.46 696.35 59.76 636.59 9323.88
47 9323.88 696.35 55.94 640.41 8683.47
48 8683.47 696.35 52.10 644.25 8039.22
49 8039.22 696.35 48.24 648.11 7391.11
50 7391.11 696.35 44.35 652.00 6739.11
51 6739.11 696.35 40.43 655.91 6083.19
52 6083.19 696.35 36.50 659.85 5423.34
53 5423.34 696.35 32.54 663.81 4759.53
54 4759.53 696.35 28.56 667.79 4091.74
55 4091.74 696.35 24.55 671.80 3419.94
56 3419.94 696.35 20.52 675.83 2744.11
57 2744.11 696.35 16.46 679.88 2064.23
58 2064.23 696.35 12.39 683.96 1380.26
59 1380.26 696.35 8.28 688.07 692.20
60 692.20 696.35 4.15 692.20 0.00
Where
Interest paid = Beginning balance * Monthly interest rate
Principal = Monthly payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Month ending balance
total payment=Monthly payment*number of Month
=696.3493*60
=41780.958
Total interest paid= total payment-period 1 beginning balance
=41780.958-35000
=6780.958

Additional interest on loan 2 = total interest on loan 2-total interest on Loan 1 = 6780.958-4454.8479=2326.11

jeff jeffy answered 2 years ago
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