In: Finance
5. You are purchasing a car today that costs $25,000. You have been given the following financing options for the car. Option 1 is conventional 4-year financing at an interest rate of 4%, compounded monthly. This option requires monthly payments. Option 2 is a balloon loan which requires monthly payments of $375 for 2 years and then a final balloon payment for the remaining balance. The interest rate on this loan is 2.5%.
a. What is the payment for the conventional loan (option 1)?
b. Prepare an amortization schedule for option 1.
c. What will the balloon payment be for the balloon loan (option 2)?
d. Prepare an amortization schedule for option 2.
e. Which option do you prefer and why? What additional considerations are there with respect to the balloon loan?
a) The Payment in case of conventional loan = 25000/(1-(1+4%/12)-48)/(4%/12) = 564.68
b)Following is the amortization table
Beginning Balance= 25000 | PMT =PMT(4%/12,12*4,-25000) | Interest part of PMT=4%/12*Beginning Principal | Principal part of PMT= PMT-Interest | Ending Balance= Beginning balance-Principal part of PMT | |
1 | $25,000.00 | $564.48 | 83.33 | $481.14 | $24,518.86 |
2 | $24,518.86 | $564.48 | 81.73 | $482.75 | $24,036.11 |
3 | $24,036.11 | $564.48 | 80.12 | $484.36 | $23,551.75 |
4 | $23,551.75 | $564.48 | 78.51 | $485.97 | $23,065.78 |
5 | $23,065.78 | $564.48 | 76.89 | $487.59 | $22,578.19 |
6 | $22,578.19 | $564.48 | 75.26 | $489.22 | $22,088.98 |
7 | $22,088.98 | $564.48 | 73.63 | $490.85 | $21,598.13 |
8 | $21,598.13 | $564.48 | 71.99 | $492.48 | $21,105.65 |
9 | $21,105.65 | $564.48 | 70.35 | $494.12 | $20,611.52 |
10 | $20,611.52 | $564.48 | 68.71 | $495.77 | $20,115.75 |
11 | $20,115.75 | $564.48 | 67.05 | $497.42 | $19,618.33 |
12 | $19,618.33 | $564.48 | 65.39 | $499.08 | $19,119.25 |
13 | $19,119.25 | $564.48 | 63.73 | $500.75 | $18,618.50 |
14 | $18,618.50 | $564.48 | 62.06 | $502.41 | $18,116.09 |
15 | $18,116.09 | $564.48 | 60.39 | $504.09 | $17,612.00 |
16 | $17,612.00 | $564.48 | 58.71 | $505.77 | $17,106.23 |
17 | $17,106.23 | $564.48 | 57.02 | $507.46 | $16,598.77 |
18 | $16,598.77 | $564.48 | 55.33 | $509.15 | $16,089.63 |
19 | $16,089.63 | $564.48 | 53.63 | $510.84 | $15,578.78 |
20 | $15,578.78 | $564.48 | 51.93 | $512.55 | $15,066.23 |
21 | $15,066.23 | $564.48 | 50.22 | $514.26 | $14,551.98 |
22 | $14,551.98 | $564.48 | 48.51 | $515.97 | $14,036.01 |
23 | $14,036.01 | $564.48 | 46.79 | $517.69 | $13,518.32 |
24 | $13,518.32 | $564.48 | 45.06 | $519.42 | $12,998.90 |
25 | $12,998.90 | $564.48 | 43.33 | $521.15 | $12,477.76 |
26 | $12,477.76 | $564.48 | 41.59 | $522.88 | $11,954.87 |
27 | $11,954.87 | $564.48 | 39.85 | $524.63 | $11,430.25 |
28 | $11,430.25 | $564.48 | 38.10 | $526.38 | $10,903.87 |
29 | $10,903.87 | $564.48 | 36.35 | $528.13 | $10,375.74 |
30 | $10,375.74 | $564.48 | 34.59 | $529.89 | $9,845.85 |
31 | $9,845.85 | $564.48 | 32.82 | $531.66 | $9,314.19 |
32 | $9,314.19 | $564.48 | 31.05 | $533.43 | $8,780.76 |
33 | $8,780.76 | $564.48 | 29.27 | $535.21 | $8,245.56 |
34 | $8,245.56 | $564.48 | 27.49 | $536.99 | $7,708.57 |
35 | $7,708.57 | $564.48 | 25.70 | $538.78 | $7,169.78 |
36 | $7,169.78 | $564.48 | 23.90 | $540.58 | $6,629.21 |
37 | $6,629.21 | $564.48 | 22.10 | $542.38 | $6,086.83 |
38 | $6,086.83 | $564.48 | 20.29 | $544.19 | $5,542.64 |
39 | $5,542.64 | $564.48 | 18.48 | $546.00 | $4,996.64 |
40 | $4,996.64 | $564.48 | 16.66 | $547.82 | $4,448.82 |
41 | $4,448.82 | $564.48 | 14.83 | $549.65 | $3,899.17 |
42 | $3,899.17 | $564.48 | 13.00 | $551.48 | $3,347.69 |
43 | $3,347.69 | $564.48 | 11.16 | $553.32 | $2,794.38 |
44 | $2,794.38 | $564.48 | 9.31 | $555.16 | $2,239.21 |
45 | $2,239.21 | $564.48 | 7.46 | $557.01 | $1,682.20 |
46 | $1,682.20 | $564.48 | 5.61 | $558.87 | $1,123.33 |
47 | $1,123.33 | $564.48 | 3.74 | $560.73 | $562.60 |
48 | $562.60 | $564.48 | 1.88 | $562.60 | ($0.00) |
c) Loan amount = 25,000
PV of annuity payment = 375*(1-(1+2.5%)-24)/2.5% =
8769.80
Balloon Payment /(1+2.5%/12)^24 = 25,000 - 8769.80
Balloon Payment = 17061.45
d)
Beginning Balance= 25000 | PMT =375 | Interest part of PMT=2.5%/12*Beginning Principal | Principal part of PMT= PMT-Interest | Ending Balance= Beginning balance-Principal part of PMT | |
1 | $25,000.00 | $375.00 | 52.08 | $322.92 | $24,677.08 |
2 | $24,677.08 | $375.00 | 51.41 | $323.59 | $24,353.49 |
3 | $24,353.49 | $375.00 | 50.74 | $324.26 | $24,029.23 |
4 | $24,029.23 | $375.00 | 50.06 | $324.94 | $23,704.29 |
5 | $23,704.29 | $375.00 | 49.38 | $325.62 | $23,378.68 |
6 | $23,378.68 | $375.00 | 48.71 | $326.29 | $23,052.38 |
7 | $23,052.38 | $375.00 | 48.03 | $326.97 | $22,725.41 |
8 | $22,725.41 | $375.00 | 47.34 | $327.66 | $22,397.75 |
9 | $22,397.75 | $375.00 | 46.66 | $328.34 | $22,069.41 |
10 | $22,069.41 | $375.00 | 45.98 | $329.02 | $21,740.39 |
11 | $21,740.39 | $375.00 | 45.29 | $329.71 | $21,410.68 |
12 | $21,410.68 | $375.00 | 44.61 | $330.39 | $21,080.29 |
13 | $21,080.29 | $375.00 | 43.92 | $331.08 | $20,749.21 |
14 | $20,749.21 | $375.00 | 43.23 | $331.77 | $20,417.43 |
15 | $20,417.43 | $375.00 | 42.54 | $332.46 | $20,084.97 |
16 | $20,084.97 | $375.00 | 41.84 | $333.16 | $19,751.81 |
17 | $19,751.81 | $375.00 | 41.15 | $333.85 | $19,417.96 |
18 | $19,417.96 | $375.00 | 40.45 | $334.55 | $19,083.42 |
19 | $19,083.42 | $375.00 | 39.76 | $335.24 | $18,748.17 |
20 | $18,748.17 | $375.00 | 39.06 | $335.94 | $18,412.23 |
21 | $18,412.23 | $375.00 | 38.36 | $336.64 | $18,075.59 |
22 | $18,075.59 | $375.00 | 37.66 | $337.34 | $17,738.25 |
23 | $17,738.25 | $375.00 | 36.95 | $338.05 | $17,400.20 |
24 | $17,400.20 | $375.00 | 36.25 | $338.75 | $17,061.45 |
Balloon Payment = 17,061.45
e) I would prefer a balloon payment because interest rate is less
by 1.5%
Other factors in balloon payment is the borrower's profile and
opportunity loss to the bank for the prepayment of loan.
Please Discuss in case of Doubt
Best of Luck. God Bless
Please Rate Well