SOLUTION: I really hate giving up here, but I can't figure out how to apply the formula and the instructor isn't answering my emails-- How long (in years) will it take to pay off a $3000

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Question 921527: I really hate giving up here, but I can't figure out how to apply the formula and the instructor isn't answering my emails--
How long (in years) will it take to pay off a $3000 loan with monthly payments of $135.14 if the add-on interest rate is 5.1%?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The total amount paid back B, is given by this formula

B+=+P+%2B+I

P = principal
I = interest

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Let t = time in months

Each monthly payment is $135.14. This is given.

Because each monthly payment is $135.14, this means that a total of 135.14t dollars will be paid back. This is the principal plus interest.

So, B+=+135.14t

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Because the add-on interest rate is 5.1%, this means that you are paying 5.1% of the principal in interest every year.

Each year, you pay 5.1% of $3000 = 0.051*3000 = 153 dollars in interest alone.

There are t months in the loan. So there are t%2F12 years in the loan.

You therefore, pay a total of I+=+153%2A%28t%2F12%29 dollars in interest alone over the entire loan.

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We are given P+=+3000

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Plug the following

B+=+135.14t
P+=+3000
I+=+153%2A%28t%2F12%29

into the formula B+=+P+%2B+I to get...


B+=+P+%2B+I


135.14t+=+3000+%2B+153%2A%28t%2F12%29


Now solve for t


135.14t+=+3000+%2B+153%2A%28t%2F12%29


135.14t+-+153%2A%28t%2F12%29+=+3000


12%2A%28135.14t+-+153%2A%28t%2F12%29%29+=+12%2A3000 Multiply both sides by 12 (to clear out the fraction).


12%2A%28135.14t%29+%2B+12%28-153%2A%28t%2F12%29%29+=+36000


1621.68t-153t+=+36000


1468.68t+=+36000


t+=+36000%2F1468.68


t+=+24.5118065201406


So it will take approximately 24.5118065201406 months. Round this up to the nearest month to get t+=+25


Now convert 25 months to years


25 months = 25/12 = 2.08333333333333 years

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Answer:

25 months

that is equivalent to

2 years, 1 month

that is equivalent to

2.08333333333333 years (approximate)


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Let me know if that helps or not. Thanks.

If you need more help, feel free to email me at jim_thompson5910@hotmail.com

My Website: http://www.freewebs.com/jimthompson5910/home.html