?Scenario: You purchased a new vehicle for $16,000 on Dec 1, 2013. Your first mo

Question

?Scenario: You purchased a new vehicle for $16,000 on Dec 1, 2013. Your first monthly payment will be due on January 1, 2014. The interest rate is 3.50% and the finance period is 4 years. Calculate now. Answer: If you calculated $692.90 or somewhere close to that, you havemade the same mistake as the student in my example. Think about how you have calculated this, and why this does not make sense. If you are questioning the interest rate, the interest rate does not say it is a monthly rate, quarterly rate, or etc; so it is a yearly rate. I worded the problem this way on purpose to help you be aware of the fact that real-life problems as well as many of the problems in Chapter 3 and on the tests are worded this way (leaving out the words “yearly rate”). Anytime a problem does not specify the rate per ??? (month, etc), then it is always a yearly rate. Re-calculate. Did you get $357.70 now or the first time? I rounded the monthly interest rate. Take the yearly rate 0.035 and divide by 12 = 0.00291666667. Always round on the second digit that repeats. So, I used 0.0029167 in my formula. In my scenario, I had the student prepare a monthly amortization schedule similar to Table 1 on page 158 in your book.

1. The amortization schedule in Figure A below is what the student prepared. Create your amortization schedule using the correct monthly payment and compare the differences.

2. How would a student determine there is a huge red flag in this answer just by using some basic calculations? Show some calculations.

3. In reality, what yearly interest rate was the formula using?

Payment Monthly Interest Unpaid Unpaid Number Balance Balance Payment Reduction 30 692.90 332.49 360.41 9,139.35 31 692.90 319.88 373.02 8,766.32 32 692.90 306.82 386.08 8,380.24 33 692.90 293.31 399.59 7,980.65 34 692.90 279.32 413.58 7,567.08 35 692.90 264.8s 428.05 7,139.02 36 692.90 249.87 443.03 6,695.99 37 692.90 234.36 458.54 6,237.45 38 692.90 21831 474.59 5,762.86 39 692.90 201.70 491.20 5,271.66 40 692.90 184.51 508.39 4,763.27 41 692.90 166.71 526.19 4,237.08 42 692.90 544.60 3,692.48 148.30 43 692.90 129.24 563.66 3,128.82 44 109.51 583.39 2,545.43 692.90 45 89.09 603.81 1,941.62 692.90 46 692.90 6796 624.94 1,316.67 47 692.90 46.08 646.82 669.86 48 693.30 23.44 669.86 0.00 33,259. 60 17,259.60 16,000.00 Totals

Explanation / Answer

Calculation of Monthly Payment:

Amount of Loan (A)

$   16,000.00

Interest rate (Monthly) = 3.50%/12 =

0.291667%

Number of Months = 4 Years * 12 =

48

Present value of $ 1 Annuity (0.291667%, 48 Periods) (B)

$44.73072

Monthly Payment   = A/B =

$357.6960

Amortization Schedule:

Payment Number

Monthly Payment

Interest

Unpaid Balance Reduction

Unpaid Balance

A

B = D*0.291667%

C= A-B

D = D - C

$16,000.0000

1

$357.6960

$46.6667

$311.0294

$15,688.9706

2

$357.6960

$45.7595

$311.9365

$15,377.0341

3

$357.6960

$44.8497

$312.8463

$15,064.1878

4

$357.6960

$43.9372

$313.7588

$14,750.4290

5

$357.6960

$43.0221

$314.6739

$14,435.7551

6

$357.6960

$42.1043

$315.5917

$14,120.1633

7

$357.6960

$41.1838

$316.5122

$13,803.6511

8

$357.6960

$40.2606

$317.4354

$13,486.2158

9

$357.6960

$39.3348

$318.3612

$13,167.8545

10

$357.6960

$38.4062

$319.2898

$12,848.5648

11

$357.6960

$37.4750

$320.2210

$12,528.3437

12

$357.6960

$36.5410

$321.1550

$12,207.1887

13

$357.6960

$35.6043

$322.0917

$11,885.0970

14

$357.6960

$34.6649

$323.0312

$11,562.0658

15

$357.6960

$33.7227

$323.9733

$11,238.0925

16

$357.6960

$32.7778

$324.9182

$10,913.1743

17

$357.6960

$31.8301

$325.8659

$10,587.3083

18

$357.6960

$30.8796

$326.8164

$10,260.4920

19

$357.6960

$29.9264

$327.7696

$9,932.7224

20

$357.6960

$28.9704

$328.7256

$9,603.9968

21

$357.6960

$28.0117

$329.6844

$9,274.3125

22

$357.6960

$27.0501

$330.6459

$8,943.6665

23

$357.6960

$26.0857

$331.6103

$8,612.0562

24

$357.6960

$25.1185

$332.5775

$8,279.4787

25

$357.6960

$24.1485

$333.5475

$7,945.9311

26

$357.6960

$23.1756

$334.5204

$7,611.4108

27

$357.6960

$22.1999

$335.4961

$7,275.9147

28

$357.6960

$21.2214

$336.4746

$6,939.4401

29

$357.6960

$20.2400

$337.4560

$6,601.9841

30

$357.6960

$19.2558

$338.4402

$6,263.5439

31

$357.6960

$18.2687

$339.4273

$5,924.1165

32

$357.6960

$17.2787

$340.4173

$5,583.6992

33

$357.6960

$16.2858

$341.4102

$5,242.2890

34

$357.6960

$15.2900

$342.4060

$4,899.8830

35

$357.6960

$14.2913

$343.4047

$4,556.4783

36

$357.6960

$13.2897

$344.4063

$4,212.0720

37

$357.6960

$12.2852

$345.4108

$3,866.6612

38

$357.6960

$11.2778

$346.4183

$3,520.2429

39

$357.6960

$10.2674

$347.4286

$3,172.8143

40

$357.6960

$9.2540

$348.4420

$2,824.3723

41

$357.6960

$8.2378

$349.4583

$2,474.9140

42

$357.6960

$7.2185

$350.4775

$2,124.4365

43

$357.6960

$6.1963

$351.4997

$1,772.9368

44

$357.6960

$5.1711

$352.5250

$1,420.4118

45

$357.6960

$4.1429

$353.5531

$1,066.8587

46

$357.6960

$3.1117

$354.5843

$712.2743

47

$357.6960

$2.0775

$355.6186

$356.6558

48

$357.6960

$1.0402

$356.6558

($0.0000)

Calculation of Monthly Payment:

Amount of Loan (A)

$   16,000.00

Interest rate (Monthly) = 3.50%/12 =

0.291667%

Number of Months = 4 Years * 12 =

48

Present value of $ 1 Annuity (0.291667%, 48 Periods) (B)

$44.73072

Monthly Payment   = A/B =

$357.6960

Amortization Schedule:

Payment Number

Monthly Payment

Interest

Unpaid Balance Reduction

Unpaid Balance

A

B = D*0.291667%

C= A-B

D = D - C

$16,000.0000

1

$357.6960

$46.6667

$311.0294

$15,688.9706

2

$357.6960

$45.7595

$311.9365

$15,377.0341

3

$357.6960

$44.8497

$312.8463

$15,064.1878

4

$357.6960

$43.9372

$313.7588

$14,750.4290

5

$357.6960

$43.0221

$314.6739

$14,435.7551

6

$357.6960

$42.1043

$315.5917

$14,120.1633

7

$357.6960

$41.1838

$316.5122

$13,803.6511

8

$357.6960

$40.2606

$317.4354

$13,486.2158

9

$357.6960

$39.3348

$318.3612

$13,167.8545

10

$357.6960

$38.4062

$319.2898

$12,848.5648

11

$357.6960

$37.4750

$320.2210

$12,528.3437

12

$357.6960

$36.5410

$321.1550

$12,207.1887

13

$357.6960

$35.6043

$322.0917

$11,885.0970

14

$357.6960

$34.6649

$323.0312

$11,562.0658

15

$357.6960

$33.7227

$323.9733

$11,238.0925

16

$357.6960

$32.7778

$324.9182

$10,913.1743

17

$357.6960

$31.8301

$325.8659

$10,587.3083

18

$357.6960

$30.8796

$326.8164

$10,260.4920

19

$357.6960

$29.9264

$327.7696

$9,932.7224

20

$357.6960

$28.9704

$328.7256

$9,603.9968

21

$357.6960

$28.0117

$329.6844

$9,274.3125

22

$357.6960

$27.0501

$330.6459

$8,943.6665

23

$357.6960

$26.0857

$331.6103

$8,612.0562

24

$357.6960

$25.1185

$332.5775

$8,279.4787

25

$357.6960

$24.1485

$333.5475

$7,945.9311

26

$357.6960

$23.1756

$334.5204

$7,611.4108

27

$357.6960

$22.1999

$335.4961

$7,275.9147

28

$357.6960

$21.2214

$336.4746

$6,939.4401

29

$357.6960

$20.2400

$337.4560

$6,601.9841

30

$357.6960

$19.2558

$338.4402

$6,263.5439

31

$357.6960

$18.2687

$339.4273

$5,924.1165

32

$357.6960

$17.2787

$340.4173

$5,583.6992

33

$357.6960

$16.2858

$341.4102

$5,242.2890

34

$357.6960

$15.2900

$342.4060

$4,899.8830

35

$357.6960

$14.2913

$343.4047

$4,556.4783

36

$357.6960

$13.2897

$344.4063

$4,212.0720

37

$357.6960

$12.2852

$345.4108

$3,866.6612

38

$357.6960

$11.2778

$346.4183

$3,520.2429

39

$357.6960

$10.2674

$347.4286

$3,172.8143

40

$357.6960

$9.2540

$348.4420

$2,824.3723

41

$357.6960

$8.2378

$349.4583

$2,474.9140

42

$357.6960

$7.2185

$350.4775

$2,124.4365

43

$357.6960

$6.1963

$351.4997

$1,772.9368

44

$357.6960

$5.1711

$352.5250

$1,420.4118

45

$357.6960

$4.1429

$353.5531

$1,066.8587

46

$357.6960

$3.1117

$354.5843

$712.2743

47

$357.6960

$2.0775

$355.6186

$356.6558

48

$357.6960

$1.0402

$356.6558

($0.0000)

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