George Costanza has just taken out an $18,351.00, 60-month car loan from his loc

Question

George Costanza has just taken out an $18,351.00, 60-month car loan from his local bank with a 5.64% interest rate compounded monthly. At the end of the second year, George plans on making a $2,625.00 payment directly to the loan’s principal and then to keep on making his regular monthly payments.

a) What is the monthly payment for this car loan? (2 decimals)

b) What is the balance remaining to pay on the loan after two years? (2 decimals)

c) What is the balance remaining on the loan after the extra payment to principal is made? (This happens after year 2...) (2 decimals)

d) How many months remain on the loan after the extra payment is made? (Do not round)

Explanation / Answer

Loan amount 18351 Maturity (in months) 60 Interest rate 5.64/12 0.4700 Annual payments (loan amount/ PVAF(0.47%,60) 0r use PMT function in excel) 351.71 Loan amortization table - Lumpsum payment at the end of year 2 or at 24th payment 2625 Year Beginning balance Monthly Payments Interest @ 0.47% Principle Ending balance 1 18351.00 351.71 86.25 265.46 18085.54 2 18085.54 351.71 85.00 266.71 17818.83 3 17818.83 351.71 83.75 267.96 17550.86 4 17550.86 351.71 82.49 269.22 17281.64 5 17281.64 351.71 81.22 270.49 17011.15 6 17011.15 351.71 79.95 271.76 16739.39 7 16739.39 351.71 78.68 273.04 16466.35 8 16466.35 351.71 77.39 274.32 16192.03 9 16192.03 351.71 76.10 275.61 15916.42 10 15916.42 351.71 74.81 276.91 15639.52 11 15639.52 351.71 73.51 278.21 15361.31 12 15361.31 351.71 72.20 279.51 15081.80 13 15081.80 351.71 70.88 280.83 14800.97 14 14800.97 351.71 69.56 282.15 14518.82 15 14518.82 351.71 68.24 283.47 14235.35 16 14235.35 351.71 66.91 284.81 13950.54 17 13950.54 351.71 65.57 286.14 13664.39 18 13664.39 351.71 64.22 287.49 13376.90 19 13376.90 351.71 62.87 288.84 13088.06 20 13088.06 351.71 61.51 290.20 12797.87 21 12797.87 351.71 60.15 291.56 12506.30 22 12506.30 351.71 58.78 292.93 12213.37 23 12213.37 351.71 57.40 294.31 11919.06 24 11919.06 351.71 56.02 295.69 11623.37 24(Additional payment) 11623.37 2625.00 0.00 2625.00 8998.37 25 8998.37 351.71 42.29 309.42 8688.95 26 8688.95 351.71 40.84 310.87 8378.07 27 8378.07 351.71 39.38 312.34 8065.74 28 8065.74 351.71 37.91 313.80 7751.93 29 7751.93 351.71 36.43 315.28 7436.66 30 7436.66 351.71 34.95 316.76 7119.89 31 7119.89 351.71 33.46 318.25 6801.65 32 6801.65 351.71 31.97 319.74 6481.90 33 6481.90 351.71 30.46 321.25 6160.65 34 6160.65 351.71 28.96 322.76 5837.90 35 5837.90 351.71 27.44 324.27 5513.62 36 5513.62 351.71 25.91 325.80 5187.82 37 5187.82 351.71 24.38 327.33 4860.49 38 4860.49 351.71 22.84 328.87 4531.63 39 4531.63 351.71 21.30 330.41 4201.21 40 4201.21 351.71 19.75 331.97 3869.24 41 3869.24 351.71 18.19 333.53 3535.72 42 3535.72 351.71 16.62 335.09 3200.62 43 3200.62 351.71 15.04 336.67 2863.95 44 2863.95 351.71 13.46 338.25 2525.70 45 2525.70 351.71 11.87 339.84 2185.86 46 2185.86 351.71 10.27 341.44 1844.42 47 1844.42 351.71 8.67 343.04 1501.38 48 1501.38 351.71 7.06 344.66 1156.72 49 1156.72 351.71 5.44 346.28 810.45 50 810.45 351.71 3.81 347.90 462.54 51 462.54 351.71 2.17 349.54 113.00 52 113.00 351.71 0.53 351.18 -238.18 53 -238.18 351.71 -1.12 352.83 -591.01 54 -591.01 351.71 -2.78 354.49 -945.50 55 -945.50 351.71 -4.44 356.16 -1301.66 56 -1301.66 351.71 -6.12 357.83 -1659.49 57 -1659.49 351.71 -7.80 359.51 -2019.00 58 -2019.00 351.71 -9.49 361.20 -2380.20 59 -2380.20 351.71 -11.19 362.90 -2743.10 60 -2743.10 351.71 -12.89 364.61 -3107.71 (i) Monthly payment = 351.71 (ii) Balance loan at the end of Year 2 (Before lumpsum payment) = 11623.37 (iii) Balance loan at the end of Year 2 (After lumpsum payment) = 8998.37 (iv) After 52nd payment the ending balance is going negative therefore the last payment is in 52nd month Time remaining for total payment after lumpsum payment = (52-24) = 28 Months 2.333333333 Years Please provide feedback…. Thanks in advance…. :-)

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