You have just purchased a car and taken out a $36.000 loan. The loan has a five

Question

You have just purchased a car and taken out a $36.000 loan. The loan has a five year term with monthly payments and an APR fss a. How much will you pay in interest, and how much will you pay in principal, during the first month, second month, and first year? (Hint: Compute the loan balance after one month, two months, and one year.) b. How much will you pay in interest, and how much will you pay in principal, during the fourth year (i.e., between three and four years from now)? (Note: Be careful not to round any intermediate steps less than six decimal places.) a. How much ill you pay in interest, and how much will you pay in principal, during the first month, second month, and first year? (Hint: Compute the loan balance after one month, two months, and one year) During the first month, you will pay s in principal. (Round to the nearest cent) During the first month, you will pay Sin interest. (Round to the nearest cent.) During the second month, you will pay $ in principal. (Round to the nearest cent During the second month, you will pay $in interest. (Round to the nearest cent) During the first year, you will pay $in principal. (Round to the nearest cent) During the frst year, you will pay s in interest. (Round to the nearest cent) b. How much will you pay in interest, and how much will you pay in principal, during the fourth year (i.e, between three During the fourth year you will pay inpm cipal. (Round the nearest cent) and four years from now)? During the fourth year, you will pay Sin interest. (Round to the nearest cent)

Explanation / Answer

Here PV = $36,000, I = 5.8%/12 and nper = 5*12 = 60 months

The monthly payment can be computed using the “PMT” function in excel.

The syntax will be: PMT (5.8%/12, 60,-36000). The monthly payment that we will get is $692.6379 or $692.64 (rounded off to 2 decimal place)

Calculations:

Interest during the 1st month = 5.8/100*1/12*36,000 = $174. Thus principal repaid = 692.64-174 = $518.64. Loan due at the end of month 1 = 36000-518.64 = 35481.36

Interest during 2nd month = 5.8/100*1/12*35481.36 = 171.49. Thus principal repaid = 692.64-171.49 = 521.14

Answers:

a. During the first month you will pay $518.64 in principal

During the first month you will pay $174.00 in interest

During the second month you will pay $521.14 in principal

During the second month you will pay $171.49 in interest

During the first year you will pay $6,391.79 in principal

During the first year you will pay $1,919.86 in interest

b. During the fourth year you will pay $7,603.40 in principal

During the fourth year you will pay $708.25 in interest.

You can refer to the loan amortization table below:

Month Opening loan balance Monthly payment Interest Principal paid during the month Loan due at the end of the month 1 36,000.00 692.64 174.00 518.64 35,481.36 2 35,481.36 692.64 171.49 521.14 34,960.22 3 34,960.22 692.64 168.97 523.66 34,436.55 4 34,436.55 692.64 166.44 526.19 33,910.36 5 33,910.36 692.64 163.90 528.74 33,381.62 6 33,381.62 692.64 161.34 531.29 32,850.33 7 32,850.33 692.64 158.78 533.86 32,316.47 8 32,316.47 692.64 156.20 536.44 31,780.03 9 31,780.03 692.64 153.60 539.03 31,240.99 10 31,240.99 692.64 151.00 541.64 30,699.35 11 30,699.35 692.64 148.38 544.26 30,155.09 12 30,155.09 692.64 145.75 546.89 29,608.21 13 29,608.21 692.64 143.11 549.53 29,058.67 14 29,058.67 692.64 140.45 552.19 28,506.49 15 28,506.49 692.64 137.78 554.86 27,951.63 16 27,951.63 692.64 135.10 557.54 27,394.09 17 27,394.09 692.64 132.40 560.23 26,833.86 18 26,833.86 692.64 129.70 562.94 26,270.92 19 26,270.92 692.64 126.98 565.66 25,705.26 20 25,705.26 692.64 124.24 568.40 25,136.86 21 25,136.86 692.64 121.49 571.14 24,565.72 22 24,565.72 692.64 118.73 573.90 23,991.81 23 23,991.81 692.64 115.96 576.68 23,415.14 24 23,415.14 692.64 113.17 579.46 22,835.67 25 22,835.67 692.64 110.37 582.27 22,253.41 26 22,253.41 692.64 107.56 585.08 21,668.33 27 21,668.33 692.64 104.73 587.91 21,080.42 28 21,080.42 692.64 101.89 590.75 20,489.67 29 20,489.67 692.64 99.03 593.60 19,896.06 30 19,896.06 692.64 96.16 596.47 19,299.59 31 19,299.59 692.64 93.28 599.36 18,700.23 32 18,700.23 692.64 90.38 602.25 18,097.98 33 18,097.98 692.64 87.47 605.16 17,492.82 34 17,492.82 692.64 84.55 608.09 16,884.73 35 16,884.73 692.64 81.61 611.03 16,273.70 36 16,273.70 692.64 78.66 613.98 15,659.72 37 15,659.72 692.64 75.69 616.95 15,042.77 38 15,042.77 692.64 72.71 619.93 14,422.84 39 14,422.84 692.64 69.71 622.93 13,799.91 40 13,799.91 692.64 66.70 625.94 13,173.97 41 13,173.97 692.64 63.67 628.96 12,545.01 42 12,545.01 692.64 60.63 632.00 11,913.00 43 11,913.00 692.64 57.58 635.06 11,277.95 44 11,277.95 692.64 54.51 638.13 10,639.82 45 10,639.82 692.64 51.43 641.21 9,998.61 46 9,998.61 692.64 48.33 644.31 9,354.29 47 9,354.29 692.64 45.21 647.43 8,706.87 48 8,706.87 692.64 42.08 650.55 8,056.31 49 8,056.31 692.64 38.94 653.70 7,402.62 50 7,402.62 692.64 35.78 656.86 6,745.76 51 6,745.76 692.64 32.60 660.03 6,085.72 52 6,085.72 692.64 29.41 663.22 5,422.50 53 5,422.50 692.64 26.21 666.43 4,756.07 54 4,756.07 692.64 22.99 669.65 4,086.42 55 4,086.42 692.64 19.75 672.89 3,413.53 56 3,413.53 692.64 16.50 676.14 2,737.39 57 2,737.39 692.64 13.23 679.41 2,057.99 58 2,057.99 692.64 9.95 682.69 1,375.30 59 1,375.30 692.64 6.65 685.99 689.31 60 689.31 692.64 3.33 689.31 0.00

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