Question 921527
The total amount paid back B, is given by this formula


{{{B = P + 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/12}}} years in the loan.


You therefore, pay a total of {{{I = 153*(t/12)}}} 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*(t/12)}}}


into the formula {{{B = P + I}}} to get...



{{{B = P + I}}}



{{{135.14t = 3000 + 153*(t/12)}}}



Now solve for t



{{{135.14t = 3000 + 153*(t/12)}}}



{{{135.14t - 153*(t/12) = 3000}}}



{{{12*(135.14t - 153*(t/12)) = 12*3000}}} Multiply both sides by 12 (to clear out the fraction).



{{{12*(135.14t) + 12(-153*(t/12)) = 36000}}}



{{{1621.68t-153t = 36000}}}



{{{1468.68t = 36000}}}



{{{t = 36000/1468.68}}}



{{{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:
<font color="red">

25 months

</font>

that is equivalent to 


<font color="red">2 years, 1 month</font>


that is equivalent to 


<font color="red">2.08333333333333 years</font> (approximate)



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Let me know if that helps or not. Thanks.


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