Help with a difference equation problem!

**JulieLYNN** · July 2nd 2009, 05:55 PM

Wanda wants to take out a loan. She can afford to make monthly payments of 200 dollars and wants to pay the loan off after exactly 30 years.
What is the maximum amount that Wanda can afford to borrow if the bank charges interest at an annual rate of 5 percent, compounded monthly?
(Give your answer, in dollars, correct to the nearest dollar.)

Help please!
Thank you!

**malaygoel** · July 2nd 2009, 06:15 PM

$P=\frac{Li}{1-e^{-nln(1+i)}}$

where
P=monthly payment...=200
L=amount borrowed...=to be found
i=monthly rate...=5/12
n=term in months..=30*12=360

now, can you continue?

**pickslides** · July 2nd 2009, 06:26 PM

$\frac{A}{30\times 12}=200$

$\frac{A}{360}=200$

$A= 72000$

now using $A=P\left(1+\frac{r}{100n}\right)^{nt}$

$72000=P\times\left(1+\frac{5}{100\times 12}\right)^{12\times 30}$

$P = \frac{72000}{\left(1+\frac{5}{100\times 12}\right)^{12\times 30}}$

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