A person takes out a a 4-year car loan of $25,000 with a fixed rate of 4.8% that

Question

A person takes out a a 4-year car loan of $25,000 with a fixed rate of 4.8% that compounds monthly. Suppose that after the first 6 months, the vehicle owner experiences a financial windfall and decides to apply $3000 towards his/her principal. (This is not a regularly scheduled payment -- this amount is in addition to the payment for month 6 in the life of the loan.)

Copy your amortization schedule from #3 and adjust it to reflect this extra payment towards the principal.

How many full months earlier will the owner be able to pay off his/her loan if he/she continues to make the original payment each month?

(amortization schedule from #3)

Period Payment Interest Paid Princ al Paid Remaing Loan Amount 25000 1 $573.47 100.00 $473.47 $24,526.53 2 573.47 98.11 S475.36 824,051.17 3 $573.47 96.20 $477.27 $23,573.90 94.30 $479.17 4 $573.47 $23,094.73 5 573.47 s 92.38 $481.09 $22,613.64 6 $573.47 90.45 $483.02 $22,130.62 7 $573.47 88.52 $484.95 $21,645.67 8 573.47 86.58 $486.89 $21,158.79 9 $573.47 84.64 $488.83 $20,669.95 82.68 $490.79 10 $573.47 $20,179.16 11 573.47 s 80.72 $492.75 $19,686.41 12 $573.47 78.75 $494.72 19,191.68 13 573.47 76.77 $496.70 $18,694.98 74,78 5498,69 14 $573.47 $18,196.29 72.79 $500.68 15 $573.47 $17,695.60 16 573.47 70.78 s 502.69 $17,192.92 17 $573.47 s 68.77 $504.70 516,688.22 66.75 $506.72 $16,181.50 18 $573.47 19 573.47 64,73 s508 74 $15,672.76 s 62.69 s 510.78 s 15,161.98 20 $573.47 21 s 573.47 60.65 $512.82 $14,649.16 22 573.47 58.60 s 514.87 $14,134.28 s 56.54 $516.93 3,617.35 23 $573.47 24 $573.47 54.47 $519.00 $13,098.35 25 573.47 s 52.39 $521.08 $12,577.27 26 $573.47 50.31 $523.16 $12,054.11 27 573.47 48.22 $525.25 $11,528.86 28 573.47 46.12 s 527.35 s 1,001.50 29 $573.47 4401 $529.46 810,472.04 30 $573.47 41.89 $531.58 $9,940.46 31 573.47 39.76 533.71 $9,406.75 32 $573.47 37.63 $535.84 $8,870.91 33 $573.47 3548 $537.99 $8,332.92 34 5573.47 s 33.33 s 540.14 $7,792.78 35 $573.47 31.17 $542.30 $7.250.48 36 573.47 29.00 s 544.47 $6,706.01 37 573.47 s 26.82 s 546.65 $6,159.37 38 $573.47 2464 $548.83 $5,610.54 22.44 s 551.03 39 $573.47 $5,059.51 40 573.47 s 20.24 $553.23 $4,506.28 411 $573.47 18.03 $555.44 $3,950.83 42 573.47 15.80 $557.67 $3,393.16 1357 s 559,90 s 2,833.27 43 $573.47 44 $573.47 11.33 $562.14 $2,271.13 s 9.08 $564.39 $1.706.75 45 $573.47 46 $573.47 6.83 $566.64 s1,140.10 47 $573.47 456 $568.91 $571.19 48 573.47 2.28 $571.19 $0.01 Total S573.47 2,526.57 $24,999.99

Explanation / Answer

Period Payment Interest Paid Principal Paid Extra Principal Paid Remaining Load Amount 0 25000 1 573.47 100 473.47 0 24526.53 2 573.47 98.11 475.36 0 24051.17 3 573.47 96.20 477.27 0 23573.90 4 573.47 94.30 479.17 0 23094.73 5 573.47 92.38 481.09 0 22613.64 6 573.47 90.45 483.02 3000 19130.62 7 573.47 76.52 496.95 0 18633.67 8 573.47 74.53 498.94 0 18134.74 9 573.47 72.54 500.93 0 17633.81 10 573.47 70.54 502.93 0 17130.87 11 573.47 68.52 504.95 0 16625.92 12 573.47 66.50 506.97 0 16118.96 13 573.47 64.48 508.99 0 15609.96 14 573.47 62.44 511.03 0 15098.93 15 573.47 60.40 513.07 0 14585.86 16 573.47 58.34 515.13 0 14070.73 17 573.47 56.28 517.19 0 13553.55 18 573.47 54.21 519.26 0 13034.29 19 573.47 52.14 521.33 0 12512.96 20 573.47 50.05 523.42 0 11989.54 21 573.47 47.96 525.51 0 11464.03 22 573.47 45.86 527.61 0 10936.41 23 573.47 43.75 529.72 0 10406.69 24 573.47 41.63 531.84 0 9874.85 25 573.47 39.50 533.97 0 9340.88 26 573.47 37.36 536.11 0 8804.77 27 573.47 35.22 538.25 0 8266.52 28 573.47 33.07 540.40 0 7726.11 29 573.47 30.90 542.57 0 7183.55 30 573.47 28.73 544.74 0 6638.81 31 573.47 26.56 546.91 0 6091.90 32 573.47 24.37 549.10 0 5542.80 33 573.47 22.17 551.30 0 4991.50 34 573.47 19.97 553.50 0 4437.99 35 573.47 17.75 555.72 0 3882.27 36 573.47 15.53 557.94 0 3324.33 37 573.47 13.30 560.17 0 2764.16 38 573.47 11.06 562.41 0 2201.75 39 573.47 8.81 564.66 0 1637.08 40 573.47 6.55 566.92 0 1070.16 41 573.47 4.28 569.19 0 500.97 42 502 2.00 500.00 0 0.98 TOTAL 2015.25 21999.02

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