Please help Financial first order differential equation

A working dog making $10000 per yr(distributed continuously) decides to buy a $40000 dog house by taking out a loan with a 10% interest rate(with interest computed continously). The dog gets a 5% salary increase per year (computed continuously), and will always make payments on his house equal to half of his salary. Assuming the dog is paid continuously and the interest rate and salary increase are computed continuously.

A) what is the dogs salary (t) yrs after the loan is made?

I got s(t)=s_{0}e^{rt }B) Give a initial value problem (differential equation and initial condition) whose solution best describes the amount of money owed by the dog (t) yrs after the loan is taken out.

C) solve the initial value prob to figure out how much is owed by the dog (t) yrs after the loan is paid (up until the date when he owes nothing).

D) can the dog afford the new dog house? When (if ever) will the loan be paid off?

Re: Please help Financial first order differential equation

For part A), you have the right form, but it is not completed.

You want to solve the IVP:

$\displaystyle \frac{ds}{dt}=ks$ where $\displaystyle 0<k\in\mathbb{R}$ and:

$\displaystyle s(0)=s_0$

$\displaystyle s(1)=(1+r_s)s_0$

$\displaystyle s_0=10000$

$\displaystyle r_s=0.05$

Once we have this nailed down, we will move on to part B).