- #1
roam
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Homework Statement
Here's a model for the balance owed on a loan with the following conditions:
* Interest accumulated on the loan at a rate of 5.24% per year
* The amount owed at the beginning of the loan was $20,000.
* No payments were made on the loan for the first two years
* After two years, the loan was paid off at $3,000 per year.
The model is given by the equations:
[itex]\frac{dL}{dt} = 0.0524 \ L, \ \ \ 0<t<2[/itex]
[itex]\frac{dL}{dt} = 0.0524 \ L \ - \ 3 , \ \ t>2[/itex]
(L is in thousands)
Using a direction field work out how large repayments should be if the loan is to be paid back in exactly 12 years (i.e., with exactly 10 years of repayments after the first two years with no repayments).
The Attempt at a Solution
Here is the direction field I made for this model
http://img210.imageshack.us/img210/1231/dfield.jpg
And the solution for the initial value L(0)=20 is
http://img703.imageshack.us/img703/1116/dfieldi.jpg
The root of this solution occurs at t=11.39, so 11 years is how long it will take to pay back the loan.
But how can we work out how large repayments should be if the loan is to be paid back in 12 years?
Any help is greatly appreciated.
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