Yes, that is the amount of the loan Clarissa can afford to borrow.

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SUMMARY

Clarissa can afford to borrow approximately $7,842.41 for her car loan based on an annual interest rate of 8% compounded continuously over a four-year term. With monthly payments of $225, the total payment over the loan period amounts to $10,800. The calculation utilizes the formula A(t) = Ke^(0.08t), where K represents the principal amount of the loan. This confirms that the derived principal amount is accurate and reflects Clarissa's borrowing capacity.

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scienceman2k9
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Problem:

Clarissa wants to buy a new car. Her loan officer tells her that her annual rate is 8%, compuded continously, over a four-year term. Clarissa informs her loan officer that she can make qual monthly payments of $225. How much can Clarissa afford to borrow?

I figured that she will pay $10800 (48 months * $225)

Skipping the differential derivation...

If A(t)=Ke^.08t ...whre t=4 and A(4)=10800...then k=$7842.41...is this the amount (principle) of the loan? I'm not accounting friendly :(
 
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