# Homework Help: Diffe equation loan problem

Tags:
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

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