In: Finance
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?
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