Question

Arnold has two loan alternatives to finance his home mortgage. The house he is interested in is for sale for $ 180,000, but he can give a prompt payment of $ 35,000. Dollar Bank offers a loan for the balance of the debt at an effective annual interest rate of 3.0% (APY), which is based on monthly payments. The loan is expected to be repaid in 15 years. The Super Cooperative offers a 3.5% annual compound rate per month and the loan is supposed to be repaid in 20 years. Required a) Make the flow chart for both alternatives. b) Evaluate both financing options and make a recommendation to Arnold. Justify your answer numerically. c) Based on his recommendation in part (b), he presumes that Arnold sticks in the lotus and decides to pay the loan halfway through the established term, having already made the first half of the payments. to. Determine the total amount to pay and Estimate interest savings.

Answer 1

Part a)

• Dollar Bank Loan Option:
  • We are given the following information:

  • r	3.00%
    n	15
    frequency	12
    PV	180,000-35,000=$145,000.00

  • We need to solve the following equation to arrive at the required PMT:
    
    1-(1+ -)-пхirequency frequency PV = PMTX frequency
    
  • 
    145000 = PMT X 1-(1+0.03 )-15x12
    
  • 
    PMT = 1001.34
    
  • So the PMT is  $1,001.34
  • Amortization schedule is given below:
  • 
    Month Opening Balance Loan PMI Interest Principal repayment Closing Balance $ 1,45,000.00 1,45,000.00 1| $ 1,45,000.00 $ 1,001.34 | $ 362.50 | ; 638.84 | $ 1,44,361.16 2[ $ 1,44,361.16 ༔ 1,001.34 | ༔ 360.30 |༔ 540.44 | ༔ 1,43,720.72 3| 1,43,720.72 1,001.34 | ; 359.30 | ; 642.04 | ༔ 1,43,078.67 4| ; 1,43,078.67 | $ 1,001.34 | 357,70 | $ 643.65 | ; 1,42,435.03 5[ $ 1,42,435.03| |$ 1,001.34 | 356.03]; 645.26 | ; 1,41,789.77 6| ; 1,41,789.77 |༔ 1,001.34 | ༔ 354.47| ; 646.87| 1,41,142.30 7| ; 1,41,142.30 $ 1,001.34 | ; 352.86 | ; 648.49 | $ 1,40,494.42 s[ $ 1,40,494.42 | $ 1,001.34 | 351.24 | $ 650.11| ; 1,39,844.31 3| ; 1,39,844.31 | $ 1,001.34 | ; 349.61| 651.73 | ; 1,39,192.58 10[ $ 1,33,192.58 | 1,001.34 | ; 347.98 | ; 653.36 | ; 1,38,539.22 11| $ 1,38,539.22 $ 1,001.34 | ; 346.35 | $ 655.00 | ; 1,37,884.22 12| 1,37,884.22 | $ 1,001.34 | 344.71 | ; 656.63 | $ 1,37,227.59 13| $ 1,37,227.59 343.07|༔ 658.27 | ; 1,36,569.31 14[ $ 1,36,569.31 | 1,001.34 | ; 341.42]; 659.32] $ 1,35,909.39 15[ $ 1,35,909.39 1,001.34 | ; 339.77| $ 661.57 1,35,247.82 16[ $ 1,35,247.82 [ $ 1,001.34 | ; 338.12|༔ 663.22 | ༔ 1,34,584.60 17| $ 1,34,584.60 | $ 1,001.34 | $ 336.46 | 664.88 | ; 1,33,913.72 18[ $ 1,33,913.72 [ $ 1,001.34 | ; 334.80 | ; 666.54 | ; 1,33,253.17 19| 1,33,253,17 $ 1,001.34 | ; 333.13 | 668.21 | ; 1,32,584.96 20[ $ 1,32,584.96 | $ 1,001.34 | 331.46 | ; 669.88 | $ 1,31,915.08 21| ; 1,31,915.08 | $ 1,001.34 | $ 323.73 | 671.56 | $ 1,31,243.53 22]; 1,31,243.53 | 1,001.34 | ; 328.11| ; 673.23 | 1,30,570.29 23|; 1,30,570.29 $ 1,001.34 | $ 326.43 | $ 674.92 |; 1,23,895.37 24| $ 1,29,895.37 ༔ 1,001.34 | ༔ 324.74 |༔ 676.60 ༔ 1,29,218.77 25[ $ 1,29,218.77 1,001.34 | $ 323.05]; 678.30 | $ 1,28,540-47 26| ༔ 1,28,540.47 | ༔ 1,001.34 | ༔ 3 21.35 |༔ 679.99 | ༔ 1,27,860.48 27[ $ 1,27,860.48 | |༔ 1,001.34 | $ 319.65 | 681.63 | $ 1,27,178.79 2[ ༔ 1,27,178.79 | 1,001.34 | 317.95 |༔ 683.40 | ; 1,26,495.33| 23| ; 1,26,495.39 | ༔ 1,001.34 | ༔ 316.24 |༔ 685.10 | ༔ 1,25,810.29 30[ $ 1,25,810.29 ༔1 ,001.34 | ༔ 314.53] 686.82 | 1,25,123.47 31| $ 1,25,123.47 $ 1,001.34 | $ 688.53 | ; 1,24,434.93 32| 1,24,434.93 1,001.34 | $ 311.09 | 33| ; 1,23,744.68 $ 1,001.34 | $ 309.36 | $ 691.98 | $ 1,23,052.70 34| ༔ 1,23,052.70 $ 1,001.34 | $ 307.63| 693.71 | 1,22,358.98 35 1,22,358.98 $ 1,001.34 | ; 305.30 | $ 695.45 | $ 1,21,663.54 36[ $ 1,21,663.54 $ 1,001.34 | ; 304.16 | ; 697,18 | 1,20,366.35 | 37| 1,20,966.35 $ 1,001.34 | ; 302.42 |༔ 698.33 | ; 1,20,267.43 38[ $ 1,20,267.43 $ 1,001.34 | $ 300.67 | 700.67| 1,13,566.75 | 39| 1,13,566.75 $ 1,001.34 | ; 298.32 | ; 702.43 | 1,18,8654.33 40[ $ 1,18,864.33 $ 1,001.34 | ; 297.16 |༔ 704.18 | 1,18,160.14 41| ; 1,18,160.14 $ 1,001.34 | ; 295.40 | $ 705.94 | ; 1,17,454.20 42[ $ 1,17,454.20 $ 1,001.34 | $ 233.644 | ; 707,71 |; 1,16,746.43| 43| 1,16,746.49 $ 1,001.34 | ; 291.87 | ; 703.48 | 1,16,037.01 44| 1,16,037.01 $ 1,001.34 | ; 290-03 | 711.25 | ; 1,15,325.76 | 45[ $ 1,15,325,76 $ 1,001.34 | $ 288.31] 713.03]; 1,14,612.73 46| $ 1,14,612.73 $ 1,001.34 | $ 286.53] 714.81 | 1,13,897.32 47| 1,13,837.32 $ 1,001.34 | $ 284.74 | ; 716.60 | 1,13,181.32 48| 1,13,181.32 $ 1,001.34 | ; 282.95 |༔ 718.33]; 1,12,462.13 43| ; 1,12,462.93 $ 1,001.34 | $ 281.16 | $ 720.19 | ; 1,11,742.75 50[ $ 1,11,742.75 $ 1,001.34 | $ 279.36 | ; 721.99 | 1,11,020.76| 51 1,11,02076 $ 1,001.34 | ; 277.55 | $ 723,79; 1,10,296.97 52[ $ 1,10,296.97 $ 1,001.34 | ; 275,74 | 725.60 | ; 1,03,571.37 53| $ 1,09,571.37 $ 1,001.34 | ; 273.93] 727.41 | ; 1,08,843.35 54| $ 1,08,843.95 $ 1,001.34 | $ 272.11]; 729.23 | 1,08,114.72 | 55[ $ 1,08,114.72 $ 1,001.34 | ; 270.29 | $ 731.06 | $ 1,07,383.66 56[ $ 1,07,383.66 $ 1,001.34 | ; 268.46 | ; 732.88 | 1,06,55078 57[ $ 1,06,55078 $ 1,001.34 | ; 266.63| ; 734.72| ; 1,05,916.06 58[ $ 1,05,916.06 $ 1,001.34 | $ 264.73 | 736.55 |; 1,05,179.51 59[ $ 1,05,173.51 $ 1,001.34 | ; 262.95 | ; 738.39 | $ 1,04,441.12 60[ $ 1,04,441.12 $ 1,001.34 | ; 261.10 | 740.24 | 1,03,700.88 61| $ 1,03,700.88 $ 1,001.34 | ; 259.25 | 742.03 | ; 1,02,958.78 62| ; 1,02,958.78 $ 1,001.34 | $ 257.40 | ; 743.35 | 1,02,214.84 63| 1,02,214,844 $ 1,001.34 | $ 255.54 | ; 745.81 | 1,01,469.03 64| ; 1,01,469.03 $ 1,001.34 | ; 253.67 | 747.67 |; 1,00,721.36 | 65[ $ 1,00,721.36 $ 1,001.34 | ; 251.80 | $ 749.54 | $ 99,971.82 66[; 99,971.82 $ 1,001.34 | $ 249.93 | ; 751.41 |༔ 99,220.41 67[ $ 33,220.41 $ 1,001.34 | ; 248.05] ; 753.29 | $ 38,467.11 68|; 38.467.11 $ 1,001.34 | ; 246.17[ $ 755.18 | 97,711.94| $ 1,001.34 | $་ 244.28 | $ 757.06 | $ 36,954.88 70| ; 96,354.88 $ 1,001.34 | $ 242.39 | ; 758.96 36,195.92 | 71[ $ 96,135.92 $ 1,001.34 | ; 240.49 | $ 760.85 | 35,435.07 72|༔ 35,435.07 $ 1,001.34 | ; 238.59 | 762.76 |; 94,672.31 73| $ 94,672.31 $ 1,001.34 | ; 236.68 | ; 764.66 33,907.65 | 74༔ 33,907.65 $ 1,001.34 | $ 234.77| ; 766.57 |; 93,141.07| 75. ; 33,141.07 $ 1,001.34 | ; 232.85 | $ 76[ $ 92.372.58 $ 1,001.34 | ; 230.93 | 770.41 ]; 91,602.17 77| ; 31,602.17 $ 1,001.34 | ; 229.01] $ 772.34 | 30,829.83 78[ $ 90,823.83 $ 1,001.34 | $ 227.07[ $ 774.27]; 90,055.56 | 73|༔ 90,055.56 $ 1,001.34 | $ 225.14 | $ 776.20 | $ 89,279.36 80| ; 89,279.36 $ 1,001.34 | ; 223.20 | ; 778.14 8 8,501.21 81|༔ 88,501.21 1,001.34 | ; 221.25 | ; 780.09 | $ 37,721.12 82[ $ 87,721.12 $ 1,001.34 | $ 213.30 [ $ 782.04 | 86,933.08 | 83|༔ 86,339.08 $ 1,001.34 | ; 217.35 | $ 784.00 | 86,155.03 84| ; 86,155.03 $ 1,001.34 | ; 215.39] 785.96 ; 85,369.13 85| ; 85,369.13 $ 1,001.34 | ; 213.42 | ; 787.32] $ 84,581.21 86[ $ 84,581.21 $ 1,001.34 | $ 211.45 | ; 789.83 | 83,791.32 | $ 1,001.34 | ; 203.48 | ; 791.87 |༔ 82,999.46 88| ; 82,999.46 $ 1,001.34 | ; 207.50 | 793.84 |༔ 82,205.61 8| ; 82,205.61 $ 1,001.34 | ; 205.51| $ 795.83 81,403.78 30[ $ 81,403.78 $ 1,001.34 | $ 203.52 | ; 797.82 | 80,611.96 91| $ 80,611.96 $ 1,001.34 | ; 201.53 | ; 92| 79,812.15 $ 1,001.34 | ; 199.53] 801.81 | ; 79,010.34 93|༔ 73,010.34 $ 1,001.34 | ; 137.53] 803.82 | $ 78,206.52 94| $ 78,206.52 $ 1,001.34 | $ 195.52 | ; 805.83 | ༔ 77,400.63 95 $ 77,400.63 $ 1,001.34 | ; 133.50 | 807.84 | 76,532.85 96| $ 76,592.85 $ 1,001.34 | ; 191.48 | ; 809.86 | $ 75,782.99 97[ $ 75,782.99 $ 1,001.34 | $ 183.46 [ $ 811.83 | $ 74,371.10 98| ; 74,971.10 $ 1,001.34 | $ 187.43 | ; 813.32]; 74,157.19 93| 74,157.19 $ 1,001.34 | ; 185.39 | ; 815.35| $ 73,341.24 100[ $ 73,341.24 $ 1,001.34 | ; 183.35 | 817.99 |༔ 72,523.25 101| $ 72,523.25 $ 1,001.34 | ; 181.31]; 820.04 | ༔ 71,703.21 102| ; 711,703.21 $ 1,001.34 | $ 179.26 | ; 822.03]; 70,881.13 103|༔ 70,881.13 $ 1,001.34 | ; 177.20 | ; 824.14 | $ 70,056.99 104| ; 70,056.99 $ 1,001.34 | ; 175,14 | ; 826.20 | $ 69,230.79 105[ $ 69,230,79 $ 1,001.34 | ; 173.08 [ $ 828.27]$ 68,402.52 106[ $ 68,402.52 $ 1,001.34 | $ 171.01 | 830.34 | $ 67,572.18 107[ $ 67,572.18 $ 1,001.34 | ; 168.93 | $ 832.41[ $ 66,733.77 108[ $ 66,733.77 $ 1,001.34 |༔ 166.85 | 834.49 | $ 65,905.27 109| ; 65,905.27 $ 1,001.34 | ; 164.76 [ $ 836.58 |༔ 65,068.63 110[ $ 65,058.59 $ 1,001.34 | $་ 162.67 | 838.67 | $ 64,230.02 111| ; 64,230.02 $ 1,001.34 | ; 160.58 | ; 840,77]; 63,383.25 112| ; 63,389.25 $ 1,001.34 | ; 158.47 | 842.87 |༔ 62,546.38 113| ; 62,546.38 $ 1,001.34 | $ 156.37 | ; 844.98 | $ 61,701.41 114| ; 61,701.41 $ 1,001.34 | $ 154.25 | ; 847.03 | $ 60,854.32 115[ $ 60,854.32 $ 1,001.34 | ; 152.14 | ; 849.21| $ 60,005.11 116| 60,005.11 $ 1,001.34 | ; 150.01] 851.33 |༔ 59,153.78 117| ; 59,153,78 $ 1,001.34 | ; 147.88 | ; 853.46 |༔ 58,300.32 118| ; 58,300.32 $ 1,001.34 | $ 145.75 | $ 855.59 |༔ 57,444.73 119| ; 57,444.73 $ 1,001.34 | ; 143.61| ; 857,73 | 56,587.00 120| ; 56,587.00 $ 1,001.34 | ; 141.47 | 859.88 |༔ 55,727.12 121| 55,727.12 $ 1,001.34 | ; 139.32 | 862.03]; 54,865,09 122| $ 54,855.03 $ 1,001.34 | $ 137.16 | $ 864.18 |༔ 54,000.91 123|༔ 54,000.91 $ 1,001.34 | ; 866.34 | 53,134.57 124| ; 53,134,57 $ 1,001.34 | $ 132.84 | ; 868.51] 52,266.07 125| ; 52,266.07 $ 1,001.34 | ; 130.67 | 870.68 | $ 51,395.39 126[ $ 51,335.39 $ 1,001.34 | $ 128.49 | ; 872.85 | $ 50,522.53| 127| 50,522.53 $ 1,001.34 | ; 126.31 | ; 875.04 | $ 49,647.50 128[ $ 49,647.50 $ 1,001.34 |༔ 124 12| 877.22]; 48,770.27 123| $ 48,770.27 $ 1,001.34 | $ 873.42 |༔ 47,890.85 130[ $ 47,830.85 $ 1,001.34 | $ 881.62 |༔ 47,009.24| 131] ; 47,003.24 $ 1,001.34 | ; 117.52 | $ 883.82 | 46,125.42 132] $ 46,125.42 $ 1,001.34 | ; 886.03 |༔ 45,239.33 133| $ 45,239.39 888.24 | $ 44,351.14 134| ; 44,351.14 $ 1,001.34 | $ 110.88 | 890.47|༔ 43,460.68 135[ $ 43,460.58 $ 1,001.34 | ; 108.65 | 892.63 | 42,567.98 136[ $ 42,567.98 $ 1,001.34 | ; 106.42 | 894.92 |༔ 41,673.06| 137| $ 41,673.06 $ 1,001.34 | $་ 104.18 | ; 837.16 |༔ 40,775.30 138| 40,775.30 $ 1,001.34 | $ 101.94 | ; 899.40 | $ 39,876.50 139| $ 39,876.50 $ 1,001.34 | ; 99.59 | 301.65 |༔ 38,974.84 140| ; 38,9744,84 $ 1,001.34 |༔ 97.44 | ; 903.31 |༔ 38,070.94 141| 38,070,94 $ 1,001.34 | ; 95.18 | $ 906.17 | $ 37,164.77 142|༔ 37,164,77 $ 1,001.34 | $ 32.31] 908.43༔ 36,256.34 143| ; 36,256.34 $ 1,001.34 | $ 90.64 | $ 910,70 | $ 35,345,64 35,345,64 | $ 1,001.34 | ; 88.36 ; 912.98 | ; 34,432.66 145| ; 34,432.66 $ 1,001.34 | $ 86.08 | ; 915.26 | $ 33,517.40 146| ; 33,517.40 $ 1,001.34 | $ 83.73 | ; 917.55 | $ 32,599.85 147[ $ 32,593.85 $ 1,001.34 | ; 81.50 | ; 913.84 | $ 31,580.00 148| ; 31,680.00 $ 1,001.34 |༔ 79.20 | 922.14 | $ 30,757.86| 30,757.86 $ 1,001.34 | ; 76.89 | ; 924.45 | ; _29,833.41 150[ $ 29,833.41 $ 1,001.34 | $ 74.58 [ $ 926.76 |༔ 28,906.65 151| $ 28,906.65 $ 1,001.34 | ; 929.08 | $ 27,377.58 152| ; 27,377,58 $ 1,001.34 | $ 69.94 |༔ 931.40 |༔ 27,046.18 153|༔ 27,046.18 $ 1,001.34 | ; 67.62 | ༔ 933.73 | ; 26,112.45 154| 26,112.45 $ 1,001.34 | $ 65.28 | 936.06 |༔ 25,176.39] 155| $ 25,176.39 $ 1,001.34 | ; 62.94 | ; 338.40 | 24,237,98 156| ; 24,237.98 $ 1,001.34 | $ 940,75| ; 23,297.23 157| ; 23,297,23 $ 1,001.34 | ; 943.10 | ; 22,354.13 158[ $་ 22,354,13 $ 1,001.34 | $ 55.89 | $ 945.46 | ; 21,408.68 159| 21,408.68 $ 1,001.34 | $ 53.52 |༔ 947.82 | $ 20,460.85 160] 20,460.85 $ 1,001.34 | ; 51.15 950.15]; 13,510.66 161| $ 19,510.66 $ 1,001.34 | $ 48.78 |༔ 952.57 | $ 18,558.10 162| ; 18,558.10 $ 1,001.34 | $ 46.40 | 954.95 | $ 17,603.15 | 163|༔ 17,603.15 $ 1,001.34 | ; 44.01] $ 957.34 | $ 16,6445.81 164| 16,645.81 $ 1,001.34 |༔ 41.61] 959.73 | $ 15,686.08 165[ $ 15,686.08 $ 1,001.34 | ; 33.22 | ; 962.13 | $ 14,723.96 166[ $ 14,723.96 $ 1,001.34 | $ 36.81]; 964.53 | $ 13,753.42 167| ; 13,759.42 $ 1,001.34 | ; 34.40 | ; 966.94 | $ 12,792.48 158[ $ 12,732.48 $ 1,001.34 | ; 31.98 | 963.36 | ; 11,823.12 169| $ 11,823.12 $ 1,001.34 | ; 29.56 | 971.79]; 10,851.33 170[ $ 10,851.33 $ 1,001.34 | $ 27,13 [ $ 974.22 | ༔ 9,877.11 171| ; 9,877.11 $ 1,001.34 | ; 24.63 |༔ 976.65 | $ 8,300.46 172[ $ 8,300-46 $ 1,001.34 | $ 22.25 | ; 379.09 |༔ 7,921.37 173| 7,921.37 $ 1,001.34 | ; 19.80 | 981.54 | $ 6,939.83 174| ; 6,339.83 $ 1,001.34 | $ 17.35 | 983.93 | $ 5,955.84 175| ; 5,955.84 $ 1,001.34 | $ 14.83 | ; 986.45 | $ 4,969.38 176$ 4,969.38 $ 1,001.34 | $ 12.42 [ $ 988.32]; 3,980.46 177[ $ 3,380.46 $ 1,001.34 | ; 9.95 991.39] $ 2,389.07 178|} 2,389.07 ; 1,001.34 | 7.47[ $ 993.87| 1,995.20 179| $ 1,395.20 $ 1,001.34 | ; 4.99 | 996.36 | 998.85 180| ; 998.85 $ 1,001.34 | ; 2.50 | ; 998.85 | $ -0.00] $ 1,80,241.81 |$ 35,241.81 |$ 1,45,000.00 149[ $
    
  • 
    1200 1000 800 600 400 200 151 157 163 169 175 Interest Value Principal repeyment value
    
• Cooperative loan:
  • We are given the following information:

  • r	3.50%
    n	20
    frequency	12
    PV	180,000-35,000=$145,000.00

  • We need to solve the following equation to arrive at the required PMT:
    
    1-(1+ -)-пхirequency frequency PV = PMTX frequency
    
  • 
    1- (1 + 0.035 -20x12 145000 = PMT X
    
  • 
    PMT = 840.94
    
  • So the PMT is  $840.94
  • Amortization schedule is given below:
  • 
    Month Opening Balance Loan PMT $ 1,45,000.00 840.94 | ડું 840.94 | ડું [2] $ 3 3 4| $ 5| $ 1,44,581.98 1,44,162.73 1,43,742.26 1,43,320.57 840.94| . 840.94| $ 840.94 . 840.94] $ 840.94 | ડું 7| $ 8| $ 9| $ 101 $ [11$ [12] $ [13] $ [14$ 15 $ 16] $ 17| $ '18 $ 19| $ 1,42,473.49 1,42,048.10 1,41,621.46 1,41,193.58 1,40,764.46 1,40,334.08 1,39,902.44 1,39,469.55 1,39,035.40 1,38,599.97 1,38,163.28 1,37,725.32 1,37,286.07 840.94] $ 840.94| . 840.94 . Principal repayment Closing Balance | $ 1,45,000.00 422.92 | ડું 418.02| $ 1,44,581.98 421.70 | ડું 419.24] $ 1,44,162.73 420.47 | ડું 421.69] $ 1,43,320.57 418.02 | ડું 422.92 | $ 1,42,897.65 416.78| $ 424.16] $ 1,42,473.49 425.39| $ 1,42,048.10 414.31 . 426.63| $ 1,41,621.46 413.06| $ 427.88| $ 1,41,193.58 411.81 | $ 429.13| $ 1,40,764.46 410.56] $ 431.63 | $ 1,39,902.44 432.89| $ 1,39,469.55 406.79] . 434.16] $ 1,39,035.40 435.42| $ 1,38,599.97 404.25| $ 436.69| $ 1,38,163.28 437.97| $ 1,37,725.32 401.70 | ડું 439.24| $ 1,37,286.07 400.42| $ 440.52| $ 1,36,845.55 441.81 | $ 1,36,403.74 397.84| $ 443.10] $ 1,35,960.64 396.55| $ 444.39] $ 1,35,516.25 395.26] $ 445.69 $ 1,35,070.57 393.96] $ 446.99| $ 1,34,623.58 448.29] $ 1,34,175.29 449.60 | $ 1,33,725.70 450.91| $ 1,33,274,79) 452.22| $ 1,32,822.56 | 840.94 | ડું 840.94| $ 840.94| . 840.94 | ડું 840.94] $ 840.94 | ડું 21| $ 22| $ 23 $ 24 $ 25| $ [26] $ 27| $ 28[ $ (29| $ |30| $ 1,36,403.74 1,35,960.64 1,35,516.25 1,35,070.57 1,34,623.58 1,34,175.29 1,33,725.70) 1,33,274.79 1,32,822.56 | 1,32,369.02 840.94 | ડું 384.75| $ 383.42| $ 382.08| $ 380.75 | $ 379.40 | ડું 378.06| $ 840.94| $ 840.94] . 840.94 | $ 840.94| $ 375.35| $ 840.94 | $ 372.63| $ 371.27 | $ 840.94] . 840.94 | $ 367.15] $ 840.94| $ 840.94] $ 364.38| $ 362.99| $ 361.59| $ 360.20 | ડું 358.79| $ 840.94| $ 840.94] $ 840.94| 840.94| $ 840.94 | $ 351.72 | ડું 350.29] $ 348.86] $ 347.43 | $ 840.94| $ 840.94| $ 343.10 | ડું 341.65| $ [32] $ 33 $ 34 $ 35| $ 36| $ 37| $ [38] $ 39 40| $ 41| $ 42| $ 43| $ 44| $ 45| $ 46| $ 47| $ 48[ $ 49| $ 50 $ 51 $ 52| $ 53| $ 54 3 55 $ 56| $ 57| $ 58[ $ 59 $ 60[ $ 61| $ 62| $ 63| $ 64 $ 65| $ [66] $ 67| $ 68| $ 69| $ 70 $ 71| $ 72 $ 73| $ 74| $ 75 $ 76| $ 77| $ 78| $ 79| $ 80| $ 81| $ 821 $ 83| $ 84| $ 85| $ 86] $ 87| $ 88| $ 89| $ 901 $ 91| $ 92| $ 93| $ 94 $ 95| $ 840.94] . 840.94 | $ 338.73| $ 1,31,457.96 1,31,000.4 1,30,541.59 1,30,081.39 1,29,619.85 1,29,156.97 1,28,692.73 1,28,227.15 1,27,760.20 1,27,291.89 1,26,822.22 1,26,351.18 1,25,878.76 1,25,404.96 1,24,929.79 1,24,453.22 1,23,975.27 1,23,495.92 1,23,015.18 1,22,533.03 1,22,049.48 1,21,564.51 1,21,078.14 1,20,590.34 1,20,101.12 1,19,610.47 1,19,118.39 1,18,624.88 1,18,129.93 1,17,633.53 1,17,135.69 1,16,636.39 1,16,135.64 1,15,633.43 1,15,129.75 1,14,624.60 1,14,117.99 1,13,609.89 1,13,100.31 1,12,589.24 1,12,076.69 1,11,562.63 1,11,047.08 1,10,530.03 1,10,011.47 1,09,491.39 1,08,969.80 1,08,446.69 1,07,922.05 1,07,395.88 1,06,868.18 1,06,338.93 1,05,808.15 1,05,275.81 1,04,741.93 1,04,206.48 1,03,669.48 1,03,130.90 1,02,590.76 1,02,049.04 1,01,505.74 1,00,960.86 1,00,41439 99,866.32 99,316.66 98,765.39 98,212.51 97,658.02 97,101.92 96,544.19 454.87| $ 1,31,914.16] 456.19| $ 1,31,457.96) 457.52| $ 1,31,000.4 458.86 | $ 1,30,541.59) 460.20] $ 1,30,081.39] 461.54] $ 1,29,619.85 462.88 | $ 1,29,156.97 464.23| $ 1,28,692.73 465.59| $ 1,28,227.15) 466.95 $ 1,27,760.20 468.31 | $ 1,27,291.89 469.67| $ 1,26,822.22 471.04| $ 1,26,351.18 472.42 | 3 1,25,878.76 473.80 | $ 1,25,404.96] 475.18| $ 1,24,929.79 476.56 | $ 1,24,453.22 477.95] $ 1,23,975.27 479.35| $ 1,23,495.92] 480.75 | $ 1,23,015.18 482.15 | $ 1,22,533.03 483.55| $ 1,22,049.48 484.96] $ 1,21,56451 486.38 | $ 1,21,078.14 487.80 | $ 1,20,590.34 489.22| $ 1,20,101.12 490.65| $ 1,19,610.47 492,08| $ 1,19,118.39 493.51| $ 1,18,624.88 494.95| $ 1,18,129.93 496.40 | $ 1,17,633.53 497.84] $ 1,17,135.69 499.30 | $ 1,16,636.39) 500.75| $ 1,16,135.64 502.21$ 1,15,633.43 503.68| $ 1,15,129.75 505.15] $ 1,14,624.60 | 506.62| $ 1,14,117.99 508.10| $ 1,13,609.89) 509.58[ $ 1,13,100.31 511.07 | $ 1,12,589.24| 512.56] $ 1,12,076.69 514.05| $ 1,11,562.63 515.55| 1,11,047.08 517.05| $ 1,10,530.03 518.56] $ 1,10,011.47 520.07 | $ 1,09,491.39] 521.59] $ 1,08,969.80 523.11| $ 1,08,446.69) 524.64| $ 1,07,922.05 526.17| $ 1,07,395.88 527.70 | $ 1,06,868.18 529.24| $ 1,06,338.93 530.79| $ 1,05,808.15 532.33| $ 1,05,275.81 533.89| $ 1,04,741.93 535.44| $ 1,04,206.48 537.01| $ 1,03,669.48 538.57| $ 1,03,130.90 | 540.14| $ 1,02,590.76 541.72 | $ 1,02,049.04| 543.30 | $ 1,01,505.74 544.88| $ 1,00,960.86 | 546.47 | $ 1,00,414.39 548.07 | ડું 99,866.32 | 549.66] $ 99,316.66 551.27 | $ 98,765.39 552.88| $ 98,212.51 554.49| $ 97,658.02 | 556.11] $ 97,101.92 557.73 | $ 96,54419] 559.35| $ 95,984.84 840.94| $ 840.94] . 331.36] $ 329.88| $ 328.39| $ 326.89| $ 840.94] . 323.89| $ 322.38| $ 320.87 | $ 319.35| $ 840.94 | ડું 840.94| $ 840.94| $ 840.94| $ 840.94| $ 840.94] . 840.94 | $ 840.94| $ 840.94| $ 840.94] . 313.24] $ 311.70 | ડું 310.16 $ 308.61] $ 307.05| $ 305.50 | ડું 302.37 | $ 300.80 | ડું 299.22] $ 840.94 | ડું 840.94| $ 840.94| $ 840.94 | $ 840.94| $ 840.94| $ 296.06] $ 294.47 | ડું 292.88| $ 291.28| $ 289.67 | $ 288.07 | $ 286.45| $ 284.84| $ 283.21$ 840.94| $ 840.94| $ 840.94| $ 840.94| $ 840.94 | $ 97| $ 100| $ 101 $ 102| 3 103 $ 104| $ 105| $ 106| 3 840.94| $ 840.94 | $ 95,423.85 94,861.23 94,296.97 93,731.06 93,163.50 92,594.28 92,023.41 91,450.87 108| $ 109| $ 110| 3 840.94| $ 840.94| $ 840.94 | $ 840.94| $ 840.94| $ 279.96] $ 278.32] $ 276.68| $ 275.03| $ 273.38| $ 271.73| $ 270.07 | $ 268.40 | ડું 266.73| $ 265.06| $ 263.38| $ 261.69 $ 260.00 | ડું 258.31| $ 112] $ 114 $ 90,300.77 89,723.21 89,143.96 88,563.02 87,980.39 87,396.06 86,810.02 840.94| $ 840.94| $ 840.94| $ 840.94 | $ 562.62| $ 564.26] $ 565.91| $ 567.56] $ 569.21$ 570.87 | $ 572.54 $ 574.21$ 575.88| $ 577.56] $ 579.25| $ 580.94| $ 582.63| $ 584.33| $ 586.04| $ 587.75| $ 589.46] $ 591.18| $ 592.90 $ 594.63| $ 596.37 | $ 598.11| $ 599.85| $ 601.60 $ 603.36] $ 605.12] $ 606.88| $ 94,861.23 94,296.97 93,731.06 | 93,163.50 | 92,594.28 92,023.41 91,450.87 90,876.66 | 90,300.77 89,723.21 89,143.96 | 88,563.02] 87,980.39 87,396.06) 86,810.02 86,222.27| 85,632.81 85,041.64 84,448.73 83,854.10 | 83,257.73 82,659.63| 82,059.77 81,458.17| 80,854.82 80,249.70 | 79,642.82 254.91 | $ 118| $ 119 $ 120| $ 840.94| $ 840.94| $ 840.94 | $ 85,632.81 249.76] $ 248.04| $ 246.31| 244.57 | $ 840.94| $ 840.94| $ 840.94 | $ 124| $ 125| $ 126] $ 83,854,10 83,257.73 82,659.63 82,059.77 81,458.17 80,854,82 241.09 $ 239.34| $ 840.94| $ 840.94] . 840.94| $ 840.94| $ 235.83 | $ 234.06] $ 232.29] $ 131| . 840.94| $ 610.43| $ 78,423.75 79,642.82 79,034.17 78,423.75 77,811.54 228.74| $ 226.95 $ 225.16] $ 223.36] $ 840.94] $ 840.94| $ 840.94| $ 840.94 | $ 134| $ 76,581.77 136| $ 219.76] $ 217.94 | $ 216.13| $ 73,475.81 72,849.18 840.94| $ 840.94| $ 840.94 | $ 840.94| $ 840.94| $ 840.94] . 840.94| $ 212.48| $ 210.64] $ 142| 3 143 $ 144 $ 71,590.41 70,958.28 613.99 $ 615.78| $ 617.58[ $ 619.38| $ 621.19] $ (623.00 | $ 624.81 | $ 626.64| $ 628.46] $ 630.30 | $ 632.14| $ 633.98| $ 635.83 | $ 637.68| $ 639.54 | $ 641.41| $ 643.28| $ 645.16] $ 647.04| $ 648.92| $ 650.82| $ 77,197.55| 76,581.77| 75,964.19 75,344.81| 74,723.63 74,100.63| 73,475.81 72,849.18 72,220.71 71,590.41 70,958.28 70,324.30) 69,688.47 69,050.79) 68,411.24 67,769.83 67,126.55| 66,481.40 | 65,834.36 65,185.44 64,534.62 146| $ 147| 148| 149| $ 150 $ 69,688.47 69,050.79 68,411.24 67,769.83 840.94| $ 840.94| $ 840.94 | $ 206.96] $ 205.11| $ 203.26] $ 201.40 | ડું 199.53| $ 197.66] $ 195.79| $ 193.90 | ડું 192.02 | $ 190.12| $ 152| $ 153 $ 65,834.36 65,185.44 64,534.62 63,881.90 63,227.28 62,570.75 840.94| $ 840.94 | $ 840.94 . 840.94| $ 840.94| $ 840.94 | $ 840.94 . 155| $ 156] $ 157| $ 158[ $ 159 $ 182.50 | ડું 180.58[ $ 178.65 | $ 654.62] $ 656.53 | $ 658.44 $ 660.36] $ 662.29| $ 664.22] $ 666.16] $ 63,227.28 62,570.75| 61,912.31 61,251.95| 60,589.66 | 59,925.43 | 59,259.28 840.94] . 840.94] $ 840.94| $ 161 $ 162| $ 163 $ 164| 3 60,589.66 59,925.43 59,259.28 58,591.17 670.05| $ 57,921.12 840.94] . 840.94 | $ 840.94] $ 840.94| $ 840.94] . 57,249.12 56,575.15 55,899.22 55,221.32 166.98| $ 673.96] $ 675.93| $ 677.90 | ડું 679.88| $ 681.86] $ 56,575.15 55,899.22 55,221.32 54,541.44 53,859.58 161.06] $ (159.08| $ 166| $ 167| $ 168| $ 169| $ 170 $ 171 ડું 172| $ 173| $ 174 $ 840.94| $ 155.10 | 840.94 | $ 840.94| $ 840.94] . 840.94| $ 176| $ 177| $ 53,859.58 53,175.73 52,489.88 51,802.04 51,112.18 50,420.32 49,726.44 49,030.53 48,332.59 47,632.62 46,930.61 46,226.55 45,520.43 44,812.26 44,102.02 43,389.71 42,675.32 41,958.85 41,240.29 40,519.63 840.94| $ 840.94| $ 840.94] $ 143.01| $ 140.97 | $ 138.93| $ 136.88| $ 134.83| $ 132.77 | $ 179| $ 180| 3 181| $ 182| $ 183 રૂં 184| $ 185| $ 186] $ 187| $ 188| $ 685.85| $ 687.85| $ 689.85| $ 691.86] $ 693.88| $ 695.91| $ 697.94 | $ 699.97| $ 702.01 $ 704.06| $ 706.11] $ 708.17| $ 710.24] $ 712.31| $ 714.39| $ 716.47 | ડું 718.56 | $ 720.66] $ 722.76] $ 724.87| $ 726.98| $ 729.10] $ 731.23| $ 52,489.88 51,802.04 | 51,112.18 50,420.32 | 49,726.44 49,030.53| 48,332.59 47,632.62| 46,930.61 46,226.55| 45,520.43 44,812.26| 44,102.02 43,389.71 42,675.32 41,958.85| 41,240.29 40,519.63| 39,796.87 39,072.01 38,345.02 37,615.92| 36,884.69 126.55] $ 120.28| $ 840.94| $ 840.94 | $ 840.94 . 840.94| $ 840.94] . 840.94| $ 840.94| $ 190 $ 191| $ 192| $ 116.07 | $ 39,072.01 38,345.02 194| $ 107.58[ $ 105.44| $ 840.94] . 101.14| $ 98.99] $ 840.94| $ 840.94 | $ 198| $ 199| $ 200| $ 201| $ 202[ $ 203 $ 32,452.32 31,706.03 92.48| $ 735.50 $ 737.65 | $ 739.80 | $ 741.95| $ 744.12| $ 746.29 | $ 748.47 | $ 750.65| $ 752.84 $ 755.03| $ 757.24 $ 759.44 $ 761.66] $ 35,415.83 34,678.19 33,938.39 33,196.44| 32,452.32 31,706.03 30,957.56 | 30,206.91 29,454.07 28,699.04 | 27,941.81 27,182.36| 26,420.70 30,206.91 29,454.07 28,699.04 205| $ 206| 3 207| 208| $ 840.94| $ 840.94| $ 840.94 | $ 840.94 | ડું 840.94| $ 840.94 | $ 840.94| $ 840.94| $ 27,182.36 25,656.82 72.60 | ડું 210| 3 211| $ 212| $ 24,122.37 840.94| $ 840.94 | $ 68.11| $ 840.94| $ 214| $ 215 . 216] $ 217| $ 218| $ 219 $_ 22,578.95 21,803.86 21,026.52 20,246.90 19,465.01 18,680.85 766.11| $ 768.34| $ 770.58| $ 772.83| $ 775.09| $ 777.35| $ 779.61] $ 781.89| $ 784.17| $ 786.46] $ 788.75| $ 791.05| $ 793.36 | $ 24,890.71 24,122.37 | 23,351.78 22,578.95| 21,803.86) 21,026.52| 20,246.90 19,465.01 18,680.85 17,894.39| 17,105.64 16,314.59) 15,521.23/ 840.94| $ 52.19 $ 840.94| $ 840.94 | $ 17,105.64 16,31459 47.58| $ 45.27| $ 221 $ 222 3 223| $ 224 $ 225| $ 840.94| $ 840.94 | $ 13,127.25 12,324.60 35.95] $ 33.60 | ડું 227| $ 840.94| $ 840.94] $ 840.94| $ 840.94 | $ 840.94| $ 840.94| $ 10,712.26 9,902.56 28.88| $ 230| 3. 232| $ 233| $ 8,276.07 7,459.27 6,640.09 800.32] $ 802.65| $ 804.99 $ 807.34| $ 809.70 | $ 812.06 | $ 814.43 | 816.80 | $ 819.19] $ 821.57 | $ 823.97 | $ 826.37 | $ 828.78| $ 831.20 | $ 833.63| $ 836.06] $ 838.50 | ડું 1,45,000.00 840.94 | $ 840.94| $ 840.94| $ 840.94| $ 840.94 | $ 840.94 | ડું 13,127.25) 12,124.60 11,519.60) 10,712.26 9,902.56 | 9,090.50 | 8,276.07 | 7,459.27 6,640.09) 5,818.51 4,994.54 4,168.17 3,339.38 2,508.18 1,67455 838.50 -0.00 | 19.37 | $ 235| $ 4,994.54 4,168.17 12.16] $ 2,508.18 237| . 238 . 239| $. 240 $ 7.32 | $ 4.88| $ 2.45 | $ 56,825.98 . 838.50 $ 2,01,825.98 | $
    
  • 
    Interest Value Principal repeyment value
    
  • Opening balance = previous year's closing balance
  • Closing balance = Opening balance+Loan-Principal repayment
  • PMT is calculated as per the above formula
    Interest = 0.03 /12 x opening balance in case of dollar bank loan and  0.035 /12 x opening balance in case of cooperative loan
  • Principal repayment = PMT - Interest

Part b) Comparison of the two loans:

Particular	Dollar bank loan	Cooperative loan
r	3.00%	3.50%
n	15	20
PMT	$1001.34	$840.94
PV	$145,000.00	$1,45,000.00
Total interest paid	$35,241.81	$56,825.98
Total of all PMTs	$1,80,241.81	$2,01,825.98

• Therefore we can see that even though the time period of the loan offered by the cooperative option is longer, ultimately the borrower ends up paying more than what he pays in the Dollar bank loan due to the effect of higher interest rate, that overpowers the impact of longer term. So Dollar bank loan is a better pick

Part c) As mentioned in the question, he goes with the Dollar bank loan and that halfway through the term, he pays off the entire loan, it means that till 7.5 years he paid in the same manner and then he made one single payment f the closing balance.

Therefore, 7.5 years = 7.5 x 12 = 90 months, at the end of which the closing balance was  $80,611.96 and till now, the total interest paid would be  $25,732.87

Total interest had he not paid it halfway would have been  $35,241.81, so the interest savings would be  $35,241.81 - $25,732.87=  $9,508.94