November 11th, 2015, 07:46 AM  #21  
Senior Member Joined: May 2008 Posts: 301 Thanks: 81  Beer soaked opinion follows. Quote:
I can't seem to find my precious notes and I forgot exactly how I arrived at the unknown loan amount; after 2 hours of contemplation, finally got an idea how I may have done it. Be back in 2 or 3 days. Got to go on a road trip. Maybe Sir Dexter will have better luck as soon as he stops filibusterng from his book of whatever.  
November 11th, 2015, 08:39 AM  #22 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Of course I'm not "right on"; I told you I rounded the final payment date from 427.0909... to 428.00 The original loan contract must call for 523 payments of 750 and a final payment of 750 * .0909... = 68.18 However, borrower needs to make that final payment on the 2.727th day of the final month (using 30 days!), so such should be part of the agreement, and also part of the agreement should be: .....else 68.18 plus interest for 30  2.727 = 27.273 days if paid on last day of month. 2.727th day means at 5:26:53 PM of 3rd day, so if receipt of payment is not dated as such, then the whole thing is out of whack and not precise...make sure your precise answer keeps that in mind, else I'll sue you!! Last edited by Denis; November 11th, 2015 at 08:48 AM. 
November 13th, 2015, 01:28 PM  #23 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
To wrap this up: amount of loan = 101,629.56025... number of months: 523.09097... owing end of 523rd month: 67.96135... final payment amount: 750 * .09097 = 68.22751... (depends on day and time payment made!) 
November 20th, 2015, 12:57 PM  #24  
Senior Member Joined: May 2008 Posts: 301 Thanks: 81  Beer soaked computations follow. Quote:
$\displaystyle 750(12)  400(1.09)^{108} = 8,524.76$ This answer (less intuitively) makes use of the fact that the entries in the principal repaid column (especially in a no rounding scenario) are in the ratio of 1 + i. A question that dawned on me at the time was whether it's possible to solve for the amount of the loan and loan term from the given information. I realized that solving for the loan amount is just a less direct way (but very intuitive way) of solving the total interest paid in the 12 installments of the 10th year. Thus, with $\displaystyle i=(1.09)^{1/12}1$ and A = loan amount, we get $\displaystyle [A(1.09)^{7}750\frac{{(1 + i)^{7(12)}  1}}{i}][A(1.09)^{8}750\frac{{(1 + i)^{8(12)}  1}}{i}] = 400$ where $\displaystyle A = 101,629.560257857...$ In this way, $\displaystyle [A(1.09)^{9}750\frac{{(1 + i)^{9(12)}  1}}{i}][A(1.09)^{10}750\frac{{(1 + i)^{10(12)}  1}}{i}] = 8,524.76$ It follows then that from $\displaystyle A=750\frac{{1  (1 + i)^{n}}}{i}$ we get n = 523.090970999108... Quote:
$\displaystyle [A(1+i)^{523}750\frac{{(1 + i)^{523}  1}}{i}](1+i)=68.4511700645338$ (This according to excel.) Management thanks you profusely for your comments and computations, Sir D.T. Sober. Rest assured that such will be duly noted in your Personnel (yes, 2 n's) File, and seriously taken in consideration at your forthcoming Annual Performance Review (not to be confused with the APR associated with financial jargon). Management also wish to apologize to Sir D.T. Sober for the late reply. Management got involved in some kind of team building thingamajig that didn't allow for beer consumption.  
November 20th, 2015, 04:52 PM  #25  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Quote:
But that's simply using the balances owing at end of: month#108: 98,780.37912... month#120: 98,305.13912... Both easily obtainable by future value formulas. 750 * 12  98780.367912 + 98305.139.12 = 8524.76 All other amount you show I agree with to the penny; so why don't I get promoted to the "decision makers group" where I can spread rumors behind your back in order to get you transferred to the mail room!! Anyhoo...perhaps I should go back to drinking: I used to think I knew everything back then But...booze gave me a loud mouth, plus disconnected it from my brain  

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