James King bought a house three years ago that cost $750,000. James put up 20% deposit and borrowed the rest from FC Bank at a rate of 7.2% per annum, compounded monthly, for 10 years.
Three months ago, FC Bank notified James that after the last monthly payment for the third year, the interest rate on his loan will increase to 9.6% per annum, compounded monthly, in line with market rates. Also, from the fourth year of his loan James can either increase the monthly repayment (so as to pay off the loan by the originally agreed date), or he can keep paying the same original monthly repayment and extend the term of the loan.
a). Total cost = 750,000
Down-payment = 20%
Mortgage amount = 750,000*(1-20%) = 600,000
Annual interest rate = 7.2% so monthly rate = 7.2%/12 = 0.60%
Duration = 10 years or 10*12 = 120 payments.
Monthly payment: I/Y = 0.60%; N = 120; PV = 600,000, solve for PMT.
PMT = 7,028.51
Loan amortization schedule for 3 years:
(a) | (b) | (c = 0.6%*a) | (d = a-c) | (e = b-d) | |
Number of payments | Monthly payment | Beg. Principal | Interest | Principal | End. Principal |
1 | 7,028.51 | 600,000.00 | 3,600.00 | 3,428.51 | 596,571.49 |
2 | 7,028.51 | 596,571.49 | 3,579.43 | 3,449.08 | 593,122.40 |
3 | 7,028.51 | 593,122.40 | 3,558.73 | 3,469.78 | 589,652.63 |
4 | 7,028.51 | 589,652.63 | 3,537.92 | 3,490.60 | 586,162.03 |
5 | 7,028.51 | 586,162.03 | 3,516.97 | 3,511.54 | 582,650.49 |
6 | 7,028.51 | 582,650.49 | 3,495.90 | 3,532.61 | 579,117.88 |
7 | 7,028.51 | 579,117.88 | 3,474.71 | 3,553.81 | 575,564.07 |
8 | 7,028.51 | 575,564.07 | 3,453.38 | 3,575.13 | 571,988.95 |
9 | 7,028.51 | 571,988.95 | 3,431.93 | 3,596.58 | 568,392.37 |
10 | 7,028.51 | 568,392.37 | 3,410.35 | 3,618.16 | 564,774.21 |
11 | 7,028.51 | 564,774.21 | 3,388.65 | 3,639.87 | 561,134.34 |
12 | 7,028.51 | 561,134.34 | 3,366.81 | 3,661.71 | 557,472.64 |
13 | 7,028.51 | 557,472.64 | 3,344.84 | 3,683.68 | 553,788.96 |
14 | 7,028.51 | 553,788.96 | 3,322.73 | 3,705.78 | 550,083.18 |
15 | 7,028.51 | 550,083.18 | 3,300.50 | 3,728.01 | 546,355.17 |
16 | 7,028.51 | 546,355.17 | 3,278.13 | 3,750.38 | 542,604.79 |
17 | 7,028.51 | 542,604.79 | 3,255.63 | 3,772.88 | 538,831.90 |
18 | 7,028.51 | 538,831.90 | 3,232.99 | 3,795.52 | 535,036.38 |
19 | 7,028.51 | 535,036.38 | 3,210.22 | 3,818.29 | 531,218.09 |
20 | 7,028.51 | 531,218.09 | 3,187.31 | 3,841.20 | 527,376.88 |
21 | 7,028.51 | 527,376.88 | 3,164.26 | 3,864.25 | 523,512.63 |
22 | 7,028.51 | 523,512.63 | 3,141.08 | 3,887.44 | 519,625.19 |
23 | 7,028.51 | 519,625.19 | 3,117.75 | 3,910.76 | 515,714.43 |
24 | 7,028.51 | 515,714.43 | 3,094.29 | 3,934.23 | 511,780.21 |
25 | 7,028.51 | 511,780.21 | 3,070.68 | 3,957.83 | 507,822.38 |
26 | 7,028.51 | 507,822.38 | 3,046.93 | 3,981.58 | 503,840.80 |
27 | 7,028.51 | 503,840.80 | 3,023.04 | 4,005.47 | 499,835.33 |
28 | 7,028.51 | 499,835.33 | 2,999.01 | 4,029.50 | 495,805.83 |
29 | 7,028.51 | 495,805.83 | 2,974.83 | 4,053.68 | 491,752.15 |
30 | 7,028.51 | 91,752.15 | 2,950.51 | 4,078.00 | 487,674.15 |
31 | 7,028.51 | 487,674.15 | 2,926.04 | 4,102.47 | 483,571.69 |
32 | 7,028.51 | 483,571.69 | 2,901.43 | 4,127.08 | 479,444.60 |
33 | 7,028.51 | 479,444.60 | 2,876.67 | 4,151.84 | 475,292.76 |
34 | 7,028.51 | 475,292.76 | 2,851.76 | 4,176.76 | 471,116.00 |
35 | 7,028.51 | 471,116.00 | 2,826.70 | 4,201.82 | 466,914.19 |
36 | 7,028.51 | 466,914.19 | 2,801.49 | 4,227.03 | 462,687.16 |
Principal remaining after 3 years = 462,687.16
New interest rate p.a. = 9.6% so monthly rate = 9.6%/12 = 0.8%
Loan duration remaining = 10-3 = 7 years or 7*12 = 84 payments
Solve for PMT: I/Y = 0.80%; N = 84; PV = 462,687.16
PMT = 7,585.87 (new monthly payment)
b). If monthly payment remains 7,028.51 then number of payments can be calculated using present value of annuity formula:
PV = PMT *(1 - (1+r)^-n)/r
PV*r/PMT = 1 - (1+r)^-n
462,687.16*0.80%/7,028.51 = 1 - (1.008)^-n
(1.008)^-n = 1 - 0.5266
1.008^-n = 0.4734
Taking log on both sides, n = 93.86
Approx.93.86 or 94 payments will be needed.
This is 94-84 = 10 payments more than the original term of the loan.
James King bought a house three years ago that cost $750,000. James put up 20% deposit and borrowed the rest from FC Bank at a rate of 7.2% per annum, compounded monthly, for 10 years. Three months ag...
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