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**mom****Member**- Registered: 2012-04-25
- Posts: 94

I am just completely lost on this one. I am not coming up with anything close to what I should be.

A mortgage at 18% interest compounded monthly with a monthly payment of $500 has an unpaid balance of $5035.56 after 109 months. Find the unpaid balance after 110 months.

I used:

i=.015

n = 110

R = $500

P = [1-(1+i)^-n/i]*R

Please help.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

Hi mom;

I am getting a principal of 27749.23 is that close?

If so then I am getting 4611.11 as the unpaid balance.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mom****Member**- Registered: 2012-04-25
- Posts: 94

Bobby,

I think so. 4611.09 was one of the options but how did you work it out?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

I used a difference equation and then solved that. Fancy talk for I made a formula.

I only worked to 2 decimals when working to more I get 4611.09 as required.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mom****Member**- Registered: 2012-04-25
- Posts: 94

thank you

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

Hi mom;

I can provide the formula if you would like. I do not know how useful it would be. perhaps if we work on it together we could make it more understandable. I know the math end but the money terms I am bad at.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mom****Member**- Registered: 2012-04-25
- Posts: 94

the formula would be awsome

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

Hi;

numberpayments = 109

interest = .18 / 12

balance = 5035.56

Plug in and you will get p = 27749.22727276801

Now you have the original mortgage.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**mom****Member**- Registered: 2012-04-25
- Posts: 94

I guess it worked but I had to figure out the total cost as it was not provided so the balance was unknown. I had to work off of the payments for 3 years at once a month and the monthly interest.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

Hi mom;

I am not exactly following you on that. I would go with the 4611.09.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**mom****Member**- Registered: 2012-04-25
- Posts: 94

Thank you for your help. I really do appreciate it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,199

Hi;

You are welcome.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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