Question
In: Finance
You have just bought a car. The $50,000 car loan from the finance company involves monthly...
You have just bought a car. The $50,000 car loan from the finance company involves monthly payments made at the end of the month, over 60 months. However, at the end of the loan, there is a lump sum payment, called a balloon payment of $30,000.
Assume the interest rate applicable is 6% p.a. monthly rest throughout the loan tenure.
(a) Discuss, using time value concepts of PV or FV of single sums, or multiple sums, etc., how you can compute the first monthly repayment. Show the computations to solve for the monthly repayment amount.
(b) Explain and compute the interest amount of the first monthly repayment.
(c) Explain and calculate the interest amount of the 13th monthly repayment.
(d) Discuss why the finance company offers the balloon scheme instead of the standard loan scheme without a balloon payment.
Note: You are to provide explanations of the computations you made. Just providing the answer from the financial calculator is not sufficient.
Solutions
Expert Solution
Using equated monthly installement formula
EMI= [P x R x (1+R)^N]/[(1+R)^N-1]
a)Hence, Monthly EMI=$536.66
b) As per the below payment schedule, interest for first payment is $ 250
c) As per the below payment schedule, interest for 13th payment is $ 232.32
d) The reason why the finance company offers the balloon scheme instead of the standard loan scheme without a balloon payment is due to high interest rate received due to Outstanding principal standing due to Balloon payment
Car Loan Repayments by Month
| Payment date | Month | Payment | Principal | Interest | Balance |
| Apr-20 | 0 | - | - | - | $50,000.00 |
| May-20 | 1 | $536.66 | $286.66 | $250.00 | $49,713.34 |
| Jun-20 | 2 | $536.66 | $288.09 | $248.57 | $49,425.25 |
| Jul-20 | 3 | $536.66 | $289.53 | $247.13 | $49,135.72 |
| Aug-20 | 4 | $536.66 | $290.98 | $245.68 | $48,844.75 |
| Sep-20 | 5 | $536.66 | $292.43 | $244.22 | $48,552.32 |
| Oct-20 | 6 | $536.66 | $293.89 | $242.76 | $48,258.42 |
| Nov-20 | 7 | $536.66 | $295.36 | $241.29 | $47,963.06 |
| Dec-20 | 8 | $536.66 | $296.84 | $239.82 | $47,666.22 |
| Jan-21 | 9 | $536.66 | $298.32 | $238.33 | $47,367.89 |
| Feb-21 | 10 | $536.66 | $299.82 | $236.84 | $47,068.07 |
| Mar-21 | 11 | $536.66 | $301.32 | $235.34 | $46,766.76 |
| Apr-21 | 12 | $536.66 | $302.82 | $233.83 | $46,463.94 |
| May-21 | 13 | $536.66 | $304.34 | $232.32 | $46,159.60 |
| Jun-21 | 14 | $536.66 | $305.86 | $230.80 | $45,853.74 |
| Jul-21 | 15 | $536.66 | $307.39 | $229.27 | $45,546.35 |
| Aug-21 | 16 | $536.66 | $308.92 | $227.73 | $45,237.43 |
| Sep-21 | 17 | $536.66 | $310.47 | $226.19 | $44,926.96 |
| Oct-21 | 18 | $536.66 | $312.02 | $224.63 | $44,614.94 |
| Nov-21 | 19 | $536.66 | $313.58 | $223.07 | $44,301.36 |
| Dec-21 | 20 | $536.66 | $315.15 | $221.51 | $43,986.21 |
| Jan-22 | 21 | $536.66 | $316.72 | $219.93 | $43,669.49 |
| Feb-22 | 22 | $536.66 | $318.31 | $218.35 | $43,351.18 |
| Mar-22 | 23 | $536.66 | $319.90 | $216.76 | $43,031.28 |
| Apr-22 | 24 | $536.66 | $321.50 | $215.16 | $42,709.78 |
| May-22 | 25 | $536.66 | $323.11 | $213.55 | $42,386.67 |
| Jun-22 | 26 | $536.66 | $324.72 | $211.93 | $42,061.95 |
| Jul-22 | 27 | $536.66 | $326.35 | $210.31 | $41,735.60 |
| Aug-22 | 28 | $536.66 | $327.98 | $208.68 | $41,407.62 |
| Sep-22 | 29 | $536.66 | $329.62 | $207.04 | $41,078.00 |
| Oct-22 | 30 | $536.66 | $331.27 | $205.39 | $40,746.74 |
| Nov-22 | 31 | $536.66 | $332.92 | $203.73 | $40,413.82 |
| Dec-22 | 32 | $536.66 | $334.59 | $202.07 | $40,079.23 |
| Jan-23 | 33 | $536.66 | $336.26 | $200.40 | $39,742.97 |
| Feb-23 | 34 | $536.66 | $337.94 | $198.71 | $39,405.03 |
| Mar-23 | 35 | $536.66 | $339.63 | $197.03 | $39,065.40 |
| Apr-23 | 36 | $536.66 | $341.33 | $195.33 | $38,724.07 |
| May-23 | 37 | $536.66 | $343.04 | $193.62 | $38,381.03 |
| Jun-23 | 38 | $536.66 | $344.75 | $191.91 | $38,036.28 |
| Jul-23 | 39 | $536.66 | $346.47 | $190.18 | $37,689.81 |
| Aug-23 | 40 | $536.66 | $348.21 | $188.45 | $37,341.60 |
| Sep-23 | 41 | $536.66 | $349.95 | $186.71 | $36,991.65 |
| Oct-23 | 42 | $536.66 | $351.70 | $184.96 | $36,639.95 |
| Nov-23 | 43 | $536.66 | $353.46 | $183.20 | $36,286.50 |
| Dec-23 | 44 | $536.66 | $355.22 | $181.43 | $35,931.27 |
| Jan-24 | 45 | $536.66 | $357.00 | $179.66 | $35,574.27 |
| Feb-24 | 46 | $536.66 | $358.78 | $177.87 | $35,215.49 |
| Mar-24 | 47 | $536.66 | $360.58 | $176.08 | $34,854.91 |
| Apr-24 | 48 | $536.66 | $362.38 | $174.27 | $34,492.53 |
| May-24 | 49 | $536.66 | $364.19 | $172.46 | $34,128.34 |
| Jun-24 | 50 | $536.66 | $366.01 | $170.64 | $33,762.32 |
| Jul-24 | 51 | $536.66 | $367.84 | $168.81 | $33,394.48 |
| Aug-24 | 52 | $536.66 | $369.68 | $166.97 | $33,024.79 |
| Sep-24 | 53 | $536.66 | $371.53 | $165.12 | $32,653.26 |
| Oct-24 | 54 | $536.66 | $373.39 | $163.27 | $32,279.87 |
| Nov-24 | 55 | $536.66 | $375.26 | $161.40 | $31,904.62 |
| Dec-24 | 56 | $536.66 | $377.13 | $159.52 | $31,527.48 |
| Jan-25 | 57 | $536.66 | $379.02 | $157.64 | $31,148.46 |
| Feb-25 | 58 | $536.66 | $380.91 | $155.74 | $30,767.55 |
| Mar-25 | 59 | $536.66 | $382.82 | $153.84 | $30,384.73 |
| Apr-25 | 60 | $536.66 | $384.73 | $151.92 | $30,000.00 |
| balloon | $30,000.00 | $30,000.00 | ---------- | $0.00 |
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