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Cooley Landscaping needs to borrow ​$26,000 for a new​ front-end dirt loader. The bank is willing...

Cooley Landscaping needs to borrow ​$26,000 for a new​ front-end dirt loader. The bank is willing to loan the money at 10​% interest for the next 7 years with annual​, semiannual​, quarterly​, or monthly payments. What are the different payments that Cooley Landscaping could choose for these different payment​ plans? What is​ Cooley's payment for the loan at 10​% interest for the next 7 years with annual ​payments?

Solutions

Expert Solution

Annual

Annual rate(M)= yearly rate= 10.00% Annual payment= 5340.54
Year Beginning balance (A) Annual payment Interest = M*A Principal paid Ending balance
1 26000.00 5340.54 2600.00 2740.54 23259.46
2 23259.46 5340.54 2325.95 3014.60 20244.86
3 20244.86 5340.54 2024.49 3316.06 16928.80
4 16928.80 5340.54 1692.88 3647.66 13281.14
5 13281.14 5340.54 1328.11 4012.43 9268.71
6 9268.71 5340.54 926.87 4413.67 4855.04
7 4855.04 5340.54 485.50 4855.04 0.00
Where
Interest paid = Beginning balance * Annual interest rate
Principal = Annual payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Year ending balance

semi annual

Semi Annual rate(M)= yearly rate/2= 5.00% Semi Annual payment= 2626.62
Half year Beginning balance (A) Semi Annual payment Interest = M*A Principal paid Ending balance
1 26000.00 2626.62 1300.00 1326.62 24673.38
2 24673.38 2626.62 1233.67 1392.95 23280.42
3 23280.42 2626.62 1164.02 1462.60 21817.82
4 21817.82 2626.62 1090.89 1535.73 20282.09
5 20282.09 2626.62 1014.10 1612.52 18669.57
6 18669.57 2626.62 933.48 1693.14 16976.42
7 16976.42 2626.62 848.82 1777.80 15198.62
8 15198.62 2626.62 759.93 1866.69 13331.93
9 13331.93 2626.62 666.60 1960.03 11371.90
10 11371.90 2626.62 568.60 2058.03 9313.88
11 9313.88 2626.62 465.69 2160.93 7152.95
12 7152.95 2626.62 357.65 2268.98 4883.97
13 4883.97 2626.62 244.20 2382.42 2501.55
14 2501.55 2626.62 125.08 2501.55 0.00
Where
Interest paid = Beginning balance * Annual interest rate
Principal = Annual payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Year ending balance

quarterly

Quarterly rate(M)= yearly rate/4= 2.50% Quarterly payment= 1302.29
Quarter Beginning balance (A) Quarterly payment Interest = M*A Principal paid Ending balance
1 26000.00 1302.29 650.00 652.29 25347.71
2 25347.71 1302.29 633.69 668.59 24679.12
3 24679.12 1302.29 616.98 685.31 23993.81
4 23993.81 1302.29 599.85 702.44 23291.37
5 23291.37 1302.29 582.28 720.00 22571.37
6 22571.37 1302.29 564.28 738.00 21833.37
7 21833.37 1302.29 545.83 756.45 21076.92
8 21076.92 1302.29 526.92 775.36 20301.55
9 20301.55 1302.29 507.54 794.75 19506.80
10 19506.80 1302.29 487.67 814.62 18692.19
11 18692.19 1302.29 467.30 834.98 17857.21
12 17857.21 1302.29 446.43 855.86 17001.35
13 17001.35 1302.29 425.03 877.25 16124.10
14 16124.10 1302.29 403.10 899.18 15224.91
15 15224.91 1302.29 380.62 921.66 14303.25
16 14303.25 1302.29 357.58 944.70 13358.55
17 13358.55 1302.29 333.96 968.32 12390.22
18 12390.22 1302.29 309.76 992.53 11397.69
19 11397.69 1302.29 284.94 1017.34 10380.35
20 10380.35 1302.29 259.51 1042.78 9337.57
21 9337.57 1302.29 233.44 1068.85 8268.72
22 8268.72 1302.29 206.72 1095.57 7173.16
23 7173.16 1302.29 179.33 1122.96 6050.20
24 6050.20 1302.29 151.25 1151.03 4899.17
25 4899.17 1302.29 122.48 1179.81 3719.36
26 3719.36 1302.29 92.98 1209.30 2510.06
27 2510.06 1302.29 62.75 1239.53 1270.52
28 1270.52 1302.29 31.76 1270.52 0.00
Where
Interest paid = Beginning balance * Annual interest rate
Principal = Annual payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Year ending balance

monthly

Monthly rate(M)= yearly rate/12= 0.83% Monthly payment= 431.63
Month Beginning balance (A) Monthly payment Interest = M*A Principal paid Ending balance
1 26000.00 431.63 216.67 214.96 25785.04
2 25785.04 431.63 214.88 216.76 25568.28
3 25568.28 431.63 213.07 218.56 25349.72
4 25349.72 431.63 211.25 220.38 25129.34
5 25129.34 431.63 209.41 222.22 24907.12
6 24907.12 431.63 207.56 224.07 24683.04
7 24683.04 431.63 205.69 225.94 24457.11
8 24457.11 431.63 203.81 227.82 24229.28

.

.

.

71 5681.36 431.63 47.34 384.29 5297.08
72 5297.08 431.63 44.14 387.49 4909.59
73 4909.59 431.63 40.91 390.72 4518.87
74 4518.87 431.63 37.66 393.97 4124.90
75 4124.90 431.63 34.37 397.26 3727.64
76 3727.64 431.63 31.06 400.57 3327.07
77 3327.07 431.63 27.73 403.91 2923.17
78 2923.17 431.63 24.36 407.27 2515.90
79 2515.90 431.63 20.97 410.66 2105.23
80 2105.23 431.63 17.54 414.09 1691.14
81 1691.14 431.63 14.09 417.54 1273.61
82 1273.61 431.63 10.61 421.02 852.59
83 852.59 431.63 7.10 424.53 428.06
84 428.06 431.63 3.57 428.06 0.00
Where
Interest paid = Beginning balance * Annual interest rate
Principal = Annual payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Year ending balance

jeff jeffy answered 1 year ago
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