Question
In: Finance
Your dream boat costs $100,000. You have $20,000 but you need to borrow the remaining $80,000....
Your dream boat costs $100,000. You have $20,000 but you need to borrow the remaining $80,000. Your bank offers you a loan with the following characteristics: APR of 5%, monthly payments, a maturity of 5 years.
Assume that you can afford the original loan the bank offered you. Now consider the last month of your loan (the last month during which you make a payment). What is your balance at the end of the month? What is your balance at the beginning of the month? How much did you pay in interest during that month? How much did you pay in amortization during that month?
Solutions
Expert Solution
EMI = Loan / PVAF (r%, n)
PVAF (r%, n) = Sum [ PVF(r%, n) ]
PVF (r%, n) = 1 /(1+r)^n
r -Int Rate per month
n - No. of Months
EMI = Loan / PVAF (r%, n)
= $ 80000 / PVAF ( 0.4167% , 60 )
= $ 80000 / 52.9907
= $ 1509.70
Loan AMortization:
| Month | Opening Balance | Instalment | Interest | Principal Repay | Clsoing Bal |
| 1 | $ 80,000.00 | $ 1,509.70 | $ 333.33 | $ 1,176.37 | $ 78,823.63 |
| 2 | $ 78,823.63 | $ 1,509.70 | $ 328.43 | $ 1,181.27 | $ 77,642.37 |
| 3 | $ 77,642.37 | $ 1,509.70 | $ 323.51 | $ 1,186.19 | $ 76,456.18 |
| 4 | $ 76,456.18 | $ 1,509.70 | $ 318.57 | $ 1,191.13 | $ 75,265.05 |
| 5 | $ 75,265.05 | $ 1,509.70 | $ 313.60 | $ 1,196.09 | $ 74,068.95 |
| 6 | $ 74,068.95 | $ 1,509.70 | $ 308.62 | $ 1,201.08 | $ 72,867.88 |
| 7 | $ 72,867.88 | $ 1,509.70 | $ 303.62 | $ 1,206.08 | $ 71,661.79 |
| 8 | $ 71,661.79 | $ 1,509.70 | $ 298.59 | $ 1,211.11 | $ 70,450.68 |
| 9 | $ 70,450.68 | $ 1,509.70 | $ 293.54 | $ 1,216.15 | $ 69,234.53 |
| 10 | $ 69,234.53 | $ 1,509.70 | $ 288.48 | $ 1,221.22 | $ 68,013.31 |
| 11 | $ 68,013.31 | $ 1,509.70 | $ 283.39 | $ 1,226.31 | $ 66,787.00 |
| 12 | $ 66,787.00 | $ 1,509.70 | $ 278.28 | $ 1,231.42 | $ 65,555.58 |
| 13 | $ 65,555.58 | $ 1,509.70 | $ 273.15 | $ 1,236.55 | $ 64,319.03 |
| 14 | $ 64,319.03 | $ 1,509.70 | $ 268.00 | $ 1,241.70 | $ 63,077.33 |
| 15 | $ 63,077.33 | $ 1,509.70 | $ 262.82 | $ 1,246.88 | $ 61,830.45 |
| 16 | $ 61,830.45 | $ 1,509.70 | $ 257.63 | $ 1,252.07 | $ 60,578.38 |
| 17 | $ 60,578.38 | $ 1,509.70 | $ 252.41 | $ 1,257.29 | $ 59,321.09 |
| 18 | $ 59,321.09 | $ 1,509.70 | $ 247.17 | $ 1,262.53 | $ 58,058.56 |
| 19 | $ 58,058.56 | $ 1,509.70 | $ 241.91 | $ 1,267.79 | $ 56,790.77 |
| 20 | $ 56,790.77 | $ 1,509.70 | $ 236.63 | $ 1,273.07 | $ 55,517.70 |
| 21 | $ 55,517.70 | $ 1,509.70 | $ 231.32 | $ 1,278.37 | $ 54,239.33 |
| 22 | $ 54,239.33 | $ 1,509.70 | $ 226.00 | $ 1,283.70 | $ 52,955.63 |
| 23 | $ 52,955.63 | $ 1,509.70 | $ 220.65 | $ 1,289.05 | $ 51,666.58 |
| 24 | $ 51,666.58 | $ 1,509.70 | $ 215.28 | $ 1,294.42 | $ 50,372.16 |
| 25 | $ 50,372.16 | $ 1,509.70 | $ 209.88 | $ 1,299.81 | $ 49,072.34 |
| 26 | $ 49,072.34 | $ 1,509.70 | $ 204.47 | $ 1,305.23 | $ 47,767.11 |
| 27 | $ 47,767.11 | $ 1,509.70 | $ 199.03 | $ 1,310.67 | $ 46,456.44 |
| 28 | $ 46,456.44 | $ 1,509.70 | $ 193.57 | $ 1,316.13 | $ 45,140.31 |
| 29 | $ 45,140.31 | $ 1,509.70 | $ 188.08 | $ 1,321.61 | $ 43,818.70 |
| 30 | $ 43,818.70 | $ 1,509.70 | $ 182.58 | $ 1,327.12 | $ 42,491.58 |
| 31 | $ 42,491.58 | $ 1,509.70 | $ 177.05 | $ 1,332.65 | $ 41,158.93 |
| 32 | $ 41,158.93 | $ 1,509.70 | $ 171.50 | $ 1,338.20 | $ 39,820.72 |
| 33 | $ 39,820.72 | $ 1,509.70 | $ 165.92 | $ 1,343.78 | $ 38,476.94 |
| 34 | $ 38,476.94 | $ 1,509.70 | $ 160.32 | $ 1,349.38 | $ 37,127.57 |
| 35 | $ 37,127.57 | $ 1,509.70 | $ 154.70 | $ 1,355.00 | $ 35,772.56 |
| 36 | $ 35,772.56 | $ 1,509.70 | $ 149.05 | $ 1,360.65 | $ 34,411.92 |
| 37 | $ 34,411.92 | $ 1,509.70 | $ 143.38 | $ 1,366.32 | $ 33,045.60 |
| 38 | $ 33,045.60 | $ 1,509.70 | $ 137.69 | $ 1,372.01 | $ 31,673.59 |
| 39 | $ 31,673.59 | $ 1,509.70 | $ 131.97 | $ 1,377.73 | $ 30,295.87 |
| 40 | $ 30,295.87 | $ 1,509.70 | $ 126.23 | $ 1,383.47 | $ 28,912.40 |
| 41 | $ 28,912.40 | $ 1,509.70 | $ 120.47 | $ 1,389.23 | $ 27,523.17 |
| 42 | $ 27,523.17 | $ 1,509.70 | $ 114.68 | $ 1,395.02 | $ 26,128.15 |
| 43 | $ 26,128.15 | $ 1,509.70 | $ 108.87 | $ 1,400.83 | $ 24,727.32 |
| 44 | $ 24,727.32 | $ 1,509.70 | $ 103.03 | $ 1,406.67 | $ 23,320.65 |
| 45 | $ 23,320.65 | $ 1,509.70 | $ 97.17 | $ 1,412.53 | $ 21,908.12 |
| 46 | $ 21,908.12 | $ 1,509.70 | $ 91.28 |
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