Upon graduation, Dixie purchases a new car. To finance the car, she borrows $20,

Question

Upon graduation, Dixie purchases a new car. To finance the car, she borrows $20,000 at 6% per year compounded monthly. The loan is to be repaid with equal monthly payments over 5 years. Show your calculations. (a) What are Dixie's monthly payments'? (h) What is the total amount of interest paid over the life of the loan? (c) flow much of the 31st payment goes to pay interest? (d) (4 points) How much of the 31st payment goes to repay principal? (e) What percentage of the amount borrowed (the $20,000) remains to be paid back after the payment that marks the halfway point in the number of payments (immediately after payment number 30)?

Explanation / Answer

a)

let x be the monthly payment

x * [1 - (1+0.06/12)^-60]/0.06/12 = 20000

x = 386.66

hence Dixie's monthly payment is 386.66

b)

total interest paid = 386.66 * 60 - 20000 = 3199.60

C)

hence 53.73 goes towards interest on 31st payment

d) hence 332.93 goes towards principal on 31st payment

e)

amount to payed back after 30th payment = 10746.74

Beginning Balance Interest Principal Ending Balance 1 $20,000.00 $100.00 $286.66 $19,713.34 2 $19,713.34 $98.57 $288.09 $19,425.25 3 $19,425.25 $97.13 $289.53 $19,135.72 4 $19,135.72 $95.68 $290.98 $18,844.75 5 $18,844.75 $94.22 $292.44 $18,552.32 6 $18,552.32 $92.76 $293.90 $18,258.42 7 $18,258.42 $91.29 $295.37 $17,963.06 8 $17,963.06 $89.82 $296.84 $17,666.22 9 $17,666.22 $88.33 $298.33 $17,367.89 10 $17,367.89 $86.84 $299.82 $17,068.07 11 $17,068.07 $85.34 $301.32 $16,766.76 12 $16,766.76 $83.83 $302.83 $16,463.94 year 1 end 13 $16,463.94 $82.32 $304.34 $16,159.60 14 $16,159.60 $80.80 $305.86 $15,853.74 15 $15,853.74 $79.27 $307.39 $15,546.35 16 $15,546.35 $77.73 $308.93 $15,237.43 17 $15,237.43 $76.19 $310.47 $14,926.96 18 $14,926.96 $74.63 $312.03 $14,614.94 19 $14,614.94 $73.07 $313.59 $14,301.36 20 $14,301.36 $71.51 $315.15 $13,986.21 21 $13,986.21 $69.93 $316.73 $13,669.49 22 $13,669.49 $68.35 $318.31 $13,351.18 23 $13,351.18 $66.76 $319.90 $13,031.28 24 $13,031.28 $65.16 $321.50 $12,709.78 year 2 end 25 $12,709.78 $63.55 $323.11 $12,386.67 26 $12,386.67 $61.93 $324.73 $12,061.95 27 $12,061.95 $60.31 $326.35 $11,735.60 28 $11,735.60 $58.68 $327.98 $11,407.62 29 $11,407.62 $57.04 $329.62 $11,078.00 30 $11,078.00 $55.39 $331.27 $10,746.74 31 $10,746.74 $53.73 $332.93 $10,413.82

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