# Diffe equation loan problem

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1. Sep 18, 2010

### hover

1. The problem statement, all variables and given/known data

# 39 on page 36, specifically part a and case 1

M(0) = $150000 ------>initial amount due M(30) =$0 -------> final amount due
r = .07
p=?

2. Relevant equations

anything to do with diffe equations

3. The attempt at a solution

Well I don't want to show all the work for it but one can find a general solution to the equation listed in the problem by dividing both sides by rM-p and by multilpying both sides by dt. So

dM/(rM-p)=dt

From here you can integrate and eventually get the general solution of

M = c*e^(r*t)+p/r

With M(0) = 150000 and M(30) = 0 I can solve for both c and p but I seem to be missing something. How do I find out how much she pays? I'm lost. Even by after checking with the answers in the back of the book I can't get the answer that they got.

Last edited by a moderator: Apr 25, 2017
2. Sep 18, 2010

### HallsofIvy

Staff Emeritus
That's the easy part! You are told that "p is the annual payment". Since she holds this loan for 30 years, she makes constant payment, p, 30 times: her total cost is 30p. Don't forget to add the three "points", .03(150,000)= \$4,500 she has to make up front for the 6.5% loan.

3. Sep 18, 2010

### hover

Wow I really overlooked this... I feel silly now. I think I was treating this problem harder than it really was because it has to do with diffe equations.

Thanks