No. That makes no difference, if it's 15, 30, or 100 year amortization. My sheet matches your table exactly.
My results show the same, but I see the balances as being at the beginning of the month. You seem to see it as at the end. I.e. beginning of Sept, balance is 31,200. Then you make the two payments.
So in Nov. 2014 the balance is 720.51. You then make your two payments, one is 597.60 (plus the insurance and taxes), the second is $126.21. Then it is paid off. In Nov. 2014. You seem to interpret it as the balance at the end of this sept is 31,200, thus the balance at the end of Nov 2014 is $720.51, meaning you send in Dec payments and it's paid off in December.
I'd still think that Nov 2014 is the correct answer, but I'm open to being wrong.
Either way, it has nothing to do with amortizing of the interest.
I'll agree with the beginning/end of month answer. Very obvious.
And I disagree that the length of amortization doesn't matter. See the table below - notice that the longer the life of the loan, the less of the payment goes to principal early on. It matters because we were given the payment amount and deduced the overpayment (extra payment to principal). If you had used a longer amortization/reamortized the loan - you'd get less bang for your overpayment buck - making me wrong in my reason for the different answers!
In summary, while I agree with your answer/work on this math problem, I disagree that amortization length doesn't matter.
Rate 5.0% Rate 5.0%
Periods 30 Periods 15
Beg Prin Int Extra End Beg Prin Int Extra End
1 100,000.00 1,505.14 5,000.00 98,494.86 1 100,000.00 4,634.23 5,000.00 - 95,365.77
2 98,494.86 1,580.40 4,924.74 - 96,914.46 2 95,365.77 4,865.94 4,768.29 - 90,499.83
3 96,914.46 1,659.42 4,845.72 - 95,255.04 3 90,499.83 5,109.24 4,524.99 - 85,390.59
4 95,255.04 1,742.39 4,762.75 - 93,512.64 4 85,390.59 5,364.70 4,269.53 - 80,025.89
5 93,512.64 1,829.51 4,675.63 - 91,683.13 5 80,025.89 5,632.93 4,001.29 - 74,392.96
6 91,683.13 1,920.99 4,584.16 - 89,762.15 6 74,392.96 5,914.58 3,719.65 - 68,478.38
7 89,762.15 2,017.04 4,488.11 - 87,745.11 7 68,478.38 6,210.31 3,423.92 - 62,268.07
8 87,745.11 2,117.89 4,387.26 - 85,627.22 8 62,268.07 6,520.83 3,113.40 - 55,747.25
9 85,627.22 2,223.78 4,281.36 - 83,403.44 9 55,747.25 6,846.87 2,787.36 - 48,900.38
10 83,403.44 2,334.97 4,170.17 - 81,068.47 10 48,900.38 7,189.21 2,445.02 - 41,711.17
11 81,068.47 2,451.72 4,053.42 - 78,616.75 11 41,711.17 7,548.67 2,085.56 - 34,162.50
12 78,616.75 2,574.31 3,930.84 - 76,042.44 12 34,162.50 7,926.10 1,708.12 - 26,236.39
13 76,042.44 2,703.02 3,802.12 - 73,339.42 13 26,236.39 8,322.41 1,311.82 - 17,913.99
14 73,339.42 2,838.17 3,666.97 - 70,501.25 14 17,913.99 8,738.53 895.70 - 9,175.46
15 70,501.25 2,980.08 3,525.06 - 67,521.17 15 9,175.46 9,175.46 458.77 - 0.00
16 67,521.17 3,129.09 3,376.06 - 64,392.08 16 - - - - -
17 64,392.08 3,285.54 3,219.60 - 61,106.54 17 - - - - -
18 61,106.54 3,449.82 3,055.33 - 57,656.72 18 - - - - -
19 57,656.72 3,622.31 2,882.84 - 54,034.42 19 - - - - -
20 54,034.42 3,803.42 2,701.72 - 50,230.99 20 - - - - -
21 50,230.99 3,993.59 2,511.55 - 46,237.40 21 - - - - -
22 46,237.40 4,193.27 2,311.87 - 42,044.13 22 - - - - -
23 42,044.13 4,402.94 2,102.21 - 37,641.19 23 - - - - -
24 37,641.19 4,623.08 1,882.06 - 33,018.11 24 - - - - -
25 33,018.11 4,854.24 1,650.91 - 28,163.87 25 - - - - -
26 28,163.87 5,096.95 1,408.19 - 23,066.92 26 - - - - -
27 23,066.92 5,351.80 1,153.35 - 17,715.12 27 - - - - -
28 17,715.12 5,619.39 885.76 - 12,095.73 28 - - - - -
29 12,095.73 5,900.36 604.79 - 6,195.37 29 - - - - -
30 6,195.37 6,195.37 309.77 - 0.00 30 - - - - -