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May 2nd, 2014, 03:37 PM  #1 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0  Financial Maths Problem
Hi, I'm having difficulty with this problem, could someone please help me out using a geometric series? "A person has a mortgage with an outstanding balance of €300,000 over a remaining period of 25 years at 5% APR. They will pay off the loan at monthly instalments at the beginning of each month. However, the person runs into financial difficulties and reaches an agreement with the bank: the bank agrees to allow the person to pay €300 off the loan per month plus the monthly interest, while extending the period of the mortgage. How many extra payments will the person have to pay now as opposed to when they were not in financial difficulty?" Thanks 
May 2nd, 2014, 07:29 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,656 Thanks: 2634 Math Focus: Mainly analysis and algebra 
Do you know what your monthly interest rate is?

May 2nd, 2014, 09:08 PM  #3  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,413 Thanks: 1024  Quote:
or is it (1 + .05/12)^12 meaning monthly compounding? And WHEN (how many months left) will the new arrangement start? Do you realise that IF this starts when 300,000 is still owing, then a principal payment of 300 per month means 300000/300 = 1000 months?!  
May 3rd, 2014, 01:28 AM  #4 
Senior Member Joined: Apr 2014 From: UK Posts: 918 Thanks: 331 
Well, the answer to this is simple. Originally it was supposed to take 25 years, 300 payments, now it's going to take 1000 payments. so that's 700 extra payments. Edit: yeah, I made some assumptions Last edited by weirddave; May 3rd, 2014 at 01:55 AM. 
May 4th, 2014, 04:20 AM  #5 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0 
How much interest in total would be paid after 1000 months?

May 4th, 2014, 07:19 AM  #6 
Senior Member Joined: Apr 2014 From: UK Posts: 918 Thanks: 331 
£943,563 That's a lot of interest! 
May 4th, 2014, 10:02 AM  #7 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0 
How did you calculate that?

May 5th, 2014, 03:36 AM  #8 
Senior Member Joined: Apr 2014 From: UK Posts: 918 Thanks: 331 
I cheated and used an online calculator

May 5th, 2014, 08:19 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,413 Thanks: 1024 
That's not correct, WDave; total interest is 625,625 1st month: 300000 * .05/12 = 1250.00 2nd month: 299700 * .05/12 = 1248.75 ... 1000th month: 300 * .05/12 = 1.25 In other words, starts at 1250.00 and gradually reduces by 1.25 each month... In other words, an easy arithmeticker: 500(1.25 + 1250.00) = 625625 Last edited by Denis; May 5th, 2014 at 08:36 AM. 
May 5th, 2014, 11:22 AM  #10 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0 
But the APR is 5%, so the equivalent monthly rate is ((1.05)^(1/12)  1)(100), not .05/12


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