The rate of change of the balance is
$
\frac{dB}{dt}=r B(t)+m
$
Here
$r$ is the interest rate and $m$ is the payment rate.
DE Poll
Work out your answer on paper or using appropriate software. Then put your answer into Webex Poll.
A college graduate would like to finance the purchase of a used Tesla S. She is able to secure a 5 year loan at an annual interest rate of 5% and she can afford monthly payments of 500. Determine the maximal price of the car she can purchase.
Put your answer into DE-Poll using two decimals
The answer is about 26,544
Solution Her yearly payments are $500\times 12=6000$ so we want to solve linear/separable differential equation
$B'=.05 B-6000$ with the initial condition $B(0)=b_0$, and determine the unknown value of $b_0$ from the condition that $B(5)=0$.
WolframAlpha
gives $B(t)=(b_0-120000) e^{0.05 t}+120000$. We want to reduce balance to 0 in 5 years, so $B(5)=0$.
WolframAlpha says $b_0= \frac{120000. e^{0.25}-120000.}{e^{0.25}}\approx 26543.9$