Question
In: Finance
A floating rate mortgage loan is made for $100,000 for a 30-year period at an initial...
A floating rate mortgage loan is made for $100,000 for a 30-year period at an initial rate of 12 percent interest. However, the borrower and lender have negotiated a monthly payment of $800. (a)What will be the loan balance at the end of year 1?
(b) What if the interest rate increases to 13 percent at the end of year 1? How much interest will be accrued as negative amortization in year 5 if the payment remains at $800?
Solutions
Expert Solution
A. Loan Balance at Year 1 End is highlighted in yellow ($ 102,536.5)
| Payment No. | Beginning Balance (A) = Ending Balance | EMI (B) | Principal E=(B-C) | Interest ('C) = A*12%/12 | Ending Balance (A-E) |
| 1 | 1,00,000.00 | 800.00 | -200.00 | 1,000.00 | 1,00,200.00 |
| 2 | 1,00,200.00 | 800.00 | -202.00 | 1,002.00 | 1,00,402.00 |
| 3 | 1,00,402.00 | 800.00 | -204.02 | 1,004.02 | 1,00,606.02 |
| 4 | 1,00,606.02 | 800.00 | -206.06 | 1,006.06 | 1,00,812.08 |
| 5 | 1,00,812.08 | 800.00 | -208.12 | 1,008.12 | 1,01,020.20 |
| 6 | 1,01,020.20 | 800.00 | -210.20 | 1,010.20 | 1,01,230.40 |
| 7 | 1,01,230.40 | 800.00 | -212.30 | 1,012.30 | 1,01,442.71 |
| 8 | 1,01,442.71 | 800.00 | -214.43 | 1,014.43 | 1,01,657.13 |
| 9 | 1,01,657.13 | 800.00 | -216.57 | 1,016.57 | 1,01,873.71 |
| 10 | 1,01,873.71 | 800.00 | -218.74 | 1,018.74 | 1,02,092.44 |
| 11 | 1,02,092.44 | 800.00 | -220.92 | 1,020.92 | 1,02,313.37 |
| 12 | 1,02,313.37 | 800.00 | -223.13 | 1,023.13 | 1,02,536.50 |
B. Below is the table provided for 60 months period, where from 13th month onwards (13%/12) rate has been used to callibrate interest.
As principal amount at 5 year end is 121,969.35, therefore 21,969.35 is the negative amortization if $800 is paid monthly.
| Payment No. | Beginning Balance (A) = Ending Balance | EMI (B) | Principal E=(B-C) | Interest ('C) = A*12%/12 | Ending Balance (A-E) |
| 1 | 1,00,000.00 | 800.00 | -200.00 | 1,000.00 | 1,00,200.00 |
| 2 | 1,00,200.00 | 800.00 | -202.00 | 1,002.00 | 1,00,402.00 |
| 3 | 1,00,402.00 | 800.00 | -204.02 | 1,004.02 | 1,00,606.02 |
| 4 | 1,00,606.02 | 800.00 | -206.06 | 1,006.06 | 1,00,812.08 |
| 5 | 1,00,812.08 | 800.00 | -208.12 | 1,008.12 | 1,01,020.20 |
| 6 | 1,01,020.20 | 800.00 | -210.20 | 1,010.20 | 1,01,230.40 |
| 7 | 1,01,230.40 | 800.00 | -212.30 | 1,012.30 | 1,01,442.71 |
| 8 | 1,01,442.71 | 800.00 | -214.43 | 1,014.43 | 1,01,657.13 |
| 9 | 1,01,657.13 | 800.00 | -216.57 | 1,016.57 | 1,01,873.71 |
| 10 | 1,01,873.71 | 800.00 | -218.74 | 1,018.74 | 1,02,092.44 |
| 11 | 1,02,092.44 | 800.00 | -220.92 | 1,020.92 | 1,02,313.37 |
| 12 | 1,02,313.37 | 800.00 | -223.13 | 1,023.13 | 1,02,536.50 |
| 13 | 1,02,536.50 | 800.00 | -310.81 | 1,110.81 | 1,02,847.31 |
| 14 | 1,02,847.31 | 800.00 | -314.18 | 1,114.18 | 1,03,161.49 |
| 15 | 1,03,161.49 | 800.00 | -317.58 | 1,117.58 | 1,03,479.07 |
| 16 | 1,03,479.07 | 800.00 | -321.02 | 1,121.02 | 1,03,800.10 |
| 17 | 1,03,800.10 | 800.00 | -324.50 | 1,124.50 | 1,04,124.60 |
| 18 | 1,04,124.60 | 800.00 | -328.02 | 1,128.02 | 1,04,452.62 |
| 19 | 1,04,452.62 | 800.00 | -331.57 | 1,131.57 | 1,04,784.19 |
| 20 | 1,04,784.19 | 800.00 | -335.16 | 1,135.16 | 1,05,119.35 |
| 21 | 1,05,119.35 | 800.00 | -338.79 | 1,138.79 | 1,05,458.14 |
| 22 | 1,05,458.14 | 800.00 | -342.46 | 1,142.46 | 1,05,800.60 |
| 23 | 1,05,800.60 | 800.00 | -346.17 | 1,146.17 | 1,06,146.78 |
| 24 | 1,06,146.78 | 800.00 | -349.92 | 1,149.92 | 1,06,496.70 |
| 25 | 1,06,496.70 | 800.00 | -353.71 | 1,153.71 | 1,06,850.41 |
| 26 | 1,06,850.41 | 800.00 | -357.55 | 1,157.55 | 1,07,207.96 |
| 27 | 1,07,207.96 | 800.00 | -361.42 | 1,161.42 | 1,07,569.38 |
| 28 | 1,07,569.38 | 800.00 | -365.33 | 1,165.33 | 1,07,934.72 |
| 29 | 1,07,934.72 | 800.00 | -369.29 | 1,169.29 | 1,08,304.01 |
| 30 | 1,08,304.01 | 800.00 | -373.29 | 1,173.29 | 1,08,677.30 |
| 31 | 1,08,677.30 | 800.00 | -377.34 | 1,177.34 | 1,09,054.64 |
| 32 | 1,09,054.64 | 800.00 | -381.43 | 1,181.43 | 1,09,436.06 |
| 33 | 1,09,436.06 | 800.00 | -385.56 | 1,185.56 | 1,09,821.62 |
| 34 | 1,09,821.62 | 800.00 | -389.73 | 1,189.73 | 1,10,211.36 |
| 35 | 1,10,211.36 | 800.00 | -393.96 | 1,193.96 | 1,10,605.31 |
| 36 | 1,10,605.31 | 800.00 | -398.22 | 1,198.22 | 1,11,003.54 |
| 37 | 1,11,003.54 | 800.00 | -402.54 | 1,202.54 | 1,11,406.07 |
| 38 | 1,11,406.07 | 800.00 | -406.90 | 1,206.90 | 1,11,812.97 |
| 39 | 1,11,812.97 | 800.00 | -411.31 | 1,211.31 | 1,12,224.28 |
| 40 | 1,12,224.28 | 800.00 | -415.76 | 1,215.76 | 1,12,640.04 |
| 41 | 1,12,640.04 | 800.00 | -420.27 | 1,220.27 | 1,13,060.31 |
| 42 | 1,13,060.31 | 800.00 | -424.82 | 1,224.82 | 1,13,485.13 |
| 43 | 1,13,485.13 | 800.00 | -429.42 | 1,229.42 | 1,13,914.55 |
| 44 | 1,13,914.55 | 800.00 | -434.07 | 1,234.07 | 1,14,348.63 |
| 45 | 1,14,348.63 | 800.00 | -438.78 | 1,238.78 | 1,14,787.40 |
| 46 | 1,14,787.40 | 800.00 | -443.53 | 1,243.53 | 1,15,230.93 |
| 47 | 1,15,230.93 | 800.00 | -448.34 | 1,248.34 | 1,15,679.27 |
| 48 | 1,15,679.27 | 800.00 | -453.19 | 1,253.19 | 1,16,132.46 |
| 49 | 1,16,132.46 | 800.00 | -458.10 | 1,258.10 | 1,16,590.56 |
| 50 | 1,16,590.56 | 800.00 | -463.06 | 1,263.06 | 1,17,053.63 |
| 51 | 1,17,053.63 | 800.00 | -468.08 | 1,268.08 | 1,17,521.71 |
| 52 | 1,17,521.71 | 800.00 | -473.15 | 1,273.15 | 1,17,994.86 |
| 53 | 1,17,994.86 | 800.00 | -478.28 | 1,278.28 | 1,18,473.14 |
| 54 | 1,18,473.14 | 800.00 | -483.46 | 1,283.46 | 1,18,956.60 |
| 55 | 1,18,956.60 | 800.00 | -488.70 | 1,288.70 | 1,19,445.29 |
| 56 | 1,19,445.29 | 800.00 | -493.99 | 1,293.99 | 1,19,939.28 |
| 57 | 1,19,939.28 | 800.00 | -499.34 | 1,299.34 | 1,20,438.63 |
| 58 | 1,20,438.63 | 800.00 | -504.75 | 1,304.75 | 1,20,943.38 |
| 59 | 1,20,943.38 | 800.00 | -510.22 | 1,310.22 | 1,21,453.60 |
| 60 | 1,21,453.60 | 800.00 | -515.75 | 1,315.75 | 1,21,969.35 |
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jeff jeffy answered 1 year agoRelated Solutions
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