A $28,000.00 car loan is to be repaid by end-of-month payments of $480.00 (except the smaller...
A $28,000.00 car loan is to be repaid by end-of-month payments of $480.00 (except the smaller concluding payment).The interest paid for the loan is 5.78 % compounded quarterly.
a) Calculate the amortization term of the car loan.
b) How much interest will be paid in the second year?
c) How much will the principal be reduced in the second year?
d) Calculate the balance after two years.
e) What will be the final payment?
Homework Answers
monthly compounded monthly
rate=(1+5.78%/4)^(4/12)-1=0.479365%
-28000+480/(0.479365%)*(1-1/(1+0.479365%)^t)=0
=>t=68.5855744418699
So, 68 payments of 480 and 1 smaller payment
Amortization term of 69 months
Interest payment in 2nd year=1284.75
Principal paid in 2nd year=4475.25
Balance after 2 years=19305.56
Final payment=446.21
| Payment | Loan beginning balance | Payment | Interest payment | Principal payment | Loan ending balance |
| 1 | 28000 | $480.00 | $137.82 | $342.18 | $27,657.82 |
| 2 | $27,657.82 | $480.00 | $136.13 | $343.87 | $27,313.95 |
| 3 | $27,313.95 | $480.00 | $134.44 | $345.56 | $26,968.39 |
| 4 | $26,968.39 | $480.00 | $132.74 | $347.26 | $26,621.13 |
| 5 | $26,621.13 | $480.00 | $131.03 | $348.97 | $26,272.17 |
| 6 | $26,272.17 | $480.00 | $129.31 | $350.69 | $25,921.48 |
| 7 | $25,921.48 | $480.00 | $127.59 | $352.41 | $25,569.07 |
| 8 | $25,569.07 | $480.00 | $125.85 | $354.15 | $25,214.92 |
| 9 | $25,214.92 | $480.00 | $124.11 | $355.89 | $24,859.03 |
| 10 | $24,859.03 | $480.00 | $122.36 | $357.64 | $24,501.39 |
| 11 | $24,501.39 | $480.00 | $120.60 | $359.40 | $24,141.98 |
| 12 | $24,141.98 | $480.00 | $118.83 | $361.17 | $23,780.81 |
| 13 | $23,780.81 | $480.00 | $117.05 | $362.95 | $23,417.86 |
| 14 | $23,417.86 | $480.00 | $115.26 | $364.74 | $23,053.13 |
| 15 | $23,053.13 | $480.00 | $113.47 | $366.53 | $22,686.60 |
| 16 | $22,686.60 | $480.00 | $111.67 | $368.33 | $22,318.26 |
| 17 | $22,318.26 | $480.00 | $109.85 | $370.15 | $21,948.12 |
| 18 | $21,948.12 | $480.00 | $108.03 | $371.97 | $21,576.15 |
| 19 | $21,576.15 | $480.00 | $106.20 | $373.80 | $21,202.35 |
| 20 | $21,202.35 | $480.00 | $104.36 | $375.64 | $20,826.71 |
| 21 | $20,826.71 | $480.00 | $102.51 | $377.49 | $20,449.22 |
| 22 | $20,449.22 | $480.00 | $100.65 | $379.35 | $20,069.87 |
| 23 | $20,069.87 | $480.00 | $98.79 | $381.21 | $19,688.65 |
| 24 | $19,688.65 | $480.00 | $96.91 | $383.09 | $19,305.56 |
| 25 | $19,305.56 | $480.00 | $95.02 | $384.98 | $18,920.59 |
| 26 | $18,920.59 | $480.00 | $93.13 | $386.87 | $18,533.72 |
| 27 | $18,533.72 | $480.00 | $91.22 | $388.78 | $18,144.94 |
| 28 | $18,144.94 | $480.00 | $89.31 | $390.69 | $17,754.25 |
| 29 | $17,754.25 | $480.00 | $87.39 | $392.61 | $17,361.64 |
| 30 | $17,361.64 | $480.00 | $85.46 | $394.54 | $16,967.09 |
| 31 | $16,967.09 | $480.00 | $83.51 | $396.49 | $16,570.61 |
| 32 | $16,570.61 | $480.00 | $81.56 | $398.44 | $16,172.17 |
| 33 | $16,172.17 | $480.00 | $79.60 | $400.40 | $15,771.77 |
| 34 | $15,771.77 | $480.00 | $77.63 | $402.37 | $15,369.40 |
| 35 | $15,369.40 | $480.00 | $75.65 | $404.35 | $14,965.05 |
| 36 | $14,965.05 | $480.00 | $73.66 | $406.34 | $14,558.71 |
| 37 | $14,558.71 | $480.00 | $71.66 | $408.34 | $14,150.37 |
| 38 | $14,150.37 | $480.00 | $69.65 | $410.35 | $13,740.02 |
| 39 | $13,740.02 | $480.00 | $67.63 | $412.37 | $13,327.65 |
| 40 | $13,327.65 | $480.00 | $65.60 | $414.40 | $12,913.24 |
| 41 | $12,913.24 | $480.00 | $63.56 | $416.44 | $12,496.80 |
| 42 | $12,496.80 | $480.00 | $61.51 | $418.49 | $12,078.32 |
| 43 | $12,078.32 | $480.00 | $59.45 | $420.55 | $11,657.77 |
| 44 | $11,657.77 | $480.00 | $57.38 | $422.62 | $11,235.15 |
| 45 | $11,235.15 | $480.00 | $55.30 | $424.70 | $10,810.45 |
| 46 | $10,810.45 | $480.00 | $53.21 | $426.79 | $10,383.66 |
| 47 | $10,383.66 | $480.00 | $51.11 | $428.89 | $9,954.77 |
| 48 | $9,954.77 | $480.00 | $49.00 | $431.00 | $9,523.76 |
| 49 | $9,523.76 | $480.00 | $46.88 | $433.12 | $9,090.64 |
| 50 | $9,090.64 | $480.00 | $44.74 | $435.26 | $8,655.38 |
| 51 | $8,655.38 | $480.00 | $42.60 | $437.40 | $8,217.99 |
| 52 | $8,217.99 | $480.00 | $40.45 | $439.55 | $7,778.44 |
| 53 | $7,778.44 | $480.00 | $38.29 | $441.71 | $7,336.72 |
| 54 | $7,336.72 | $480.00 | $36.11 | $443.89 | $6,892.83 |
| 55 | $6,892.83 | $480.00 | $33.93 | $446.07 | $6,446.76 |
| 56 | $6,446.76 | $480.00 | $31.73 | $448.27 | $5,998.49 |
| 57 | $5,998.49 | $480.00 | $29.53 | $450.47 | $5,548.02 |
| 58 | $5,548.02 | $480.00 | $27.31 | $452.69 | $5,095.33 |
| 59 | $5,095.33 | $480.00 | $25.08 | $454.92 | $4,640.41 |
| 60 | $4,640.41 | $480.00 | $22.84 | $457.16 | $4,183.25 |
| 61 | $4,183.25 | $480.00 | $20.59 | $459.41 | $3,723.84 |
| 62 | $3,723.84 | $480.00 | $18.33 | $461.67 | $3,262.17 |
| 63 | $3,262.17 | $480.00 | $16.06 | $463.94 | $2,798.22 |
| 64 | $2,798.22 | $480.00 | $13.77 | $466.23 | $2,332.00 |
| 65 | $2,332.00 | $480.00 | $11.48 | $468.52 | $1,863.47 |
| 66 | $1,863.47 | $480.00 | $9.17 | $470.83 | $1,392.65 |
| 67 | $1,392.65 | $480.00 | $6.85 | $473.15 | $919.50 |
| 68 | $919.50 | $480.00 | $4.53 | $475.47 | $444.03 |
| 69 | $444.03 | $446.21 | $2.19 | $444.03 | $0.00 |
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