Hank purchased a $28,000 car two years ago using an 8 percent, 5-year loan. how much...
Hank purchased a $28,000 car two years ago using an 8 percent, 5-year loan. how much principle did Hank pay during the 12 months he had his car?
Homework Answers
We are given the following information:
| r | 8.00% |
| n | 5 |
| frequency | 12 |
| PV | $ 28,000.00 |
We need to solve the following equation to arrive at the required PMT
So the monthly PMT is 567.74
We will have the below amortization schedule:
| Month | Opening Balance | PMT | Interest | Principal repayment | Closing Balance |
| 0 | $ 28,000.00 | ||||
| 1 | $ 28,000.00 | $ 567.74 | $ 186.67 | $ 381.07 | $ 27,618.93 |
| 2 | $ 27,618.93 | $ 567.74 | $ 184.13 | $ 383.61 | $ 27,235.31 |
| 3 | $ 27,235.31 | $ 567.74 | $ 181.57 | $ 386.17 | $ 26,849.14 |
| 4 | $ 26,849.14 | $ 567.74 | $ 178.99 | $ 388.74 | $ 26,460.40 |
| 5 | $ 26,460.40 | $ 567.74 | $ 176.40 | $ 391.34 | $ 26,069.06 |
| 6 | $ 26,069.06 | $ 567.74 | $ 173.79 | $ 393.95 | $ 25,675.12 |
| 7 | $ 25,675.12 | $ 567.74 | $ 171.17 | $ 396.57 | $ 25,278.55 |
| 8 | $ 25,278.55 | $ 567.74 | $ 168.52 | $ 399.22 | $ 24,879.33 |
| 9 | $ 24,879.33 | $ 567.74 | $ 165.86 | $ 401.88 | $ 24,477.45 |
| 10 | $ 24,477.45 | $ 567.74 | $ 163.18 | $ 404.56 | $ 24,072.90 |
| 11 | $ 24,072.90 | $ 567.74 | $ 160.49 | $ 407.25 | $ 23,665.65 |
| 12 | $ 23,665.65 | $ 567.74 | $ 157.77 | $ 409.97 | $ 23,255.68 |
| 13 | $ 23,255.68 | $ 567.74 | $ 155.04 | $ 412.70 | $ 22,842.98 |
| 14 | $ 22,842.98 | $ 567.74 | $ 152.29 | $ 415.45 | $ 22,427.52 |
| 15 | $ 22,427.52 | $ 567.74 | $ 149.52 | $ 418.22 | $ 22,009.30 |
| 16 | $ 22,009.30 | $ 567.74 | $ 146.73 | $ 421.01 | $ 21,588.29 |
| 17 | $ 21,588.29 | $ 567.74 | $ 143.92 | $ 423.82 | $ 21,164.47 |
| 18 | $ 21,164.47 | $ 567.74 | $ 141.10 | $ 426.64 | $ 20,737.83 |
| 19 | $ 20,737.83 | $ 567.74 | $ 138.25 | $ 429.49 | $ 20,308.34 |
| 20 | $ 20,308.34 | $ 567.74 | $ 135.39 | $ 432.35 | $ 19,875.99 |
| 21 | $ 19,875.99 | $ 567.74 | $ 132.51 | $ 435.23 | $ 19,440.76 |
| 22 | $ 19,440.76 | $ 567.74 | $ 129.61 | $ 438.13 | $ 19,002.63 |
| 23 | $ 19,002.63 | $ 567.74 | $ 126.68 | $ 441.05 | $ 18,561.57 |
| 24 | $ 18,561.57 | $ 567.74 | $ 123.74 | $ 444.00 | $ 18,117.58 |
| 25 | $ 18,117.58 | $ 567.74 | $ 120.78 | $ 446.96 | $ 17,670.62 |
| 26 | $ 17,670.62 | $ 567.74 | $ 117.80 | $ 449.93 | $ 17,220.69 |
| 27 | $ 17,220.69 | $ 567.74 | $ 114.80 | $ 452.93 | $ 16,767.75 |
| 28 | $ 16,767.75 | $ 567.74 | $ 111.79 | $ 455.95 | $ 16,311.80 |
| 29 | $ 16,311.80 | $ 567.74 | $ 108.75 | $ 458.99 | $ 15,852.81 |
| 30 | $ 15,852.81 | $ 567.74 | $ 105.69 | $ 462.05 | $ 15,390.75 |
| 31 | $ 15,390.75 | $ 567.74 | $ 102.61 | $ 465.13 | $ 14,925.62 |
| 32 | $ 14,925.62 | $ 567.74 | $ 99.50 | $ 468.23 | $ 14,457.38 |
| 33 | $ 14,457.38 | $ 567.74 | $ 96.38 | $ 471.36 | $ 13,986.03 |
| 34 | $ 13,986.03 | $ 567.74 | $ 93.24 | $ 474.50 | $ 13,511.53 |
| 35 | $ 13,511.53 | $ 567.74 | $ 90.08 | $ 477.66 | $ 13,033.87 |
| 36 | $ 13,033.87 | $ 567.74 | $ 86.89 | $ 480.85 | $ 12,553.02 |
| 37 | $ 12,553.02 | $ 567.74 | $ 83.69 | $ 484.05 | $ 12,068.97 |
| 38 | $ 12,068.97 | $ 567.74 | $ 80.46 | $ 487.28 | $ 11,581.69 |
| 39 | $ 11,581.69 | $ 567.74 | $ 77.21 | $ 490.53 | $ 11,091.16 |
| 40 | $ 11,091.16 | $ 567.74 | $ 73.94 | $ 493.80 | $ 10,597.36 |
| 41 | $ 10,597.36 | $ 567.74 | $ 70.65 | $ 497.09 | $ 10,100.27 |
| 42 | $ 10,100.27 | $ 567.74 | $ 67.34 | $ 500.40 | $ 9,599.87 |
| 43 | $ 9,599.87 | $ 567.74 | $ 64.00 | $ 503.74 | $ 9,096.13 |
| 44 | $ 9,096.13 | $ 567.74 | $ 60.64 | $ 507.10 | $ 8,589.03 |
| 45 | $ 8,589.03 | $ 567.74 | $ 57.26 | $ 510.48 | $ 8,078.55 |
| 46 | $ 8,078.55 | $ 567.74 | $ 53.86 | $ 513.88 | $ 7,564.67 |
| 47 | $ 7,564.67 | $ 567.74 | $ 50.43 | $ 517.31 | $ 7,047.36 |
| 48 | $ 7,047.36 | $ 567.74 | $ 46.98 | $ 520.76 | $ 6,526.60 |
| 49 | $ 6,526.60 | $ 567.74 | $ 43.51 | $ 524.23 | $ 6,002.38 |
| 50 | $ 6,002.38 | $ 567.74 | $ 40.02 | $ 527.72 | $ 5,474.65 |
| 51 | $ 5,474.65 | $ 567.74 | $ 36.50 | $ 531.24 | $ 4,943.41 |
| 52 | $ 4,943.41 | $ 567.74 | $ 32.96 | $ 534.78 | $ 4,408.63 |
| 53 | $ 4,408.63 | $ 567.74 | $ 29.39 | $ 538.35 | $ 3,870.28 |
| 54 | $ 3,870.28 | $ 567.74 | $ 25.80 | $ 541.94 | $ 3,328.34 |
| 55 | $ 3,328.34 | $ 567.74 | $ 22.19 | $ 545.55 | $ 2,782.79 |
| 56 | $ 2,782.79 | $ 567.74 | $ 18.55 | $ 549.19 | $ 2,233.61 |
| 57 | $ 2,233.61 | $ 567.74 | $ 14.89 | $ 552.85 | $ 1,680.76 |
| 58 | $ 1,680.76 | $ 567.74 | $ 11.21 | $ 556.53 | $ 1,124.22 |
| 59 | $ 1,124.22 | $ 567.74 | $ 7.49 | $ 560.24 | $ 563.98 |
| 60 | $ 563.98 | $ 567.74 | $ 3.76 | $ 563.98 | $ -0.00 |
| $ 34,064.34 | $ 6,064.34 | $ 28,000.00 |
- Opening balance = previous year's closing balance
- Closing balance = Opening balance-Principal repayment
- PMT is calculated as per the above formula
- Interest = 0.08 /12 x opening balance
- Principal repayment = PMT - Interest
- We are given that the car was purchased 2 years ago so it has been with hank for 24 months and not 12 months. Closing balance at the end of 24th month is $18,117.58 so the total principal repayment= original loan - $18,117.58 = 28000- $18,117.58 = $9,882.42
- However if it is required to calculate after 12 months. we can look at the closing balance at the end of 12 months , which is $23,255.68, so the repayment = 28000 - $23,255.68 = $4,744.32
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