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 loan of 1200 has annual interest rate of 3%. Determine the monthly payment that will pay it off in 5 years.
Assume continuous payments and continuous compounding. Put your answer into DE-Poll using two decimals
The answer is $\approx 21.54$.
Solution Monthly interest rate is $r=\frac{.03}{12}=\frac{3}{1200}$ so we want to solve differential equation
$B'=\frac{3}{1200}B-m$ with the initial condition $B(0)=1200$. WolframAlpha
gives ugly answer $B(t)=-400 (e^{t/400} (-3 + m) - m)$. We want to reduce balance to 0 in 60 month so $B(60)=0$.
WolframAlpha says $m=\frac{3 e^{3/20}}{e^{3/20}-1}\approx 21.5375$