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May 2nd, 2014, 03:37 PM   #1
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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?"

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May 2nd, 2014, 07:29 PM   #2
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Do you know what your monthly interest rate is?
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May 2nd, 2014, 09:08 PM   #3
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Quote:
Originally Posted by Marko1011 View Post
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?"
As Archie asked... is the 5% APR compounding annually,
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?!
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May 3rd, 2014, 01:28 AM   #4
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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.
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May 4th, 2014, 04:20 AM   #5
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How much interest in total would be paid after 1000 months?
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May 4th, 2014, 07:19 AM   #6
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£943,563
That's a lot of interest!
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May 4th, 2014, 10:02 AM   #7
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How did you calculate that?
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May 5th, 2014, 03:36 AM   #8
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I cheated and used an online calculator
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May 5th, 2014, 08:19 AM   #9
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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.
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May 5th, 2014, 11:22 AM   #10
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But the APR is 5%, so the equivalent monthly rate is ((1.05)^(1/12) - 1)(100), not .05/12
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