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 freshmen would like to purchase of a used Tessla S as a graduation present for himself in 5 years. He decides to save 500 a month for 5 years, which he invests in CDs that bring annual interest rate of 5%. Determine the price of the car he can purchase.
Put your answer into DE-Poll using two decimals
The answer is about 34,083
Solution His yearly savings are $500\times 12=6000$, so we want to solve
$B'=.05 B+6000$ with the initial condition $B(0)=0$, and determine the value of $B(5)$.
WolframAlpha
gives $B(t)=-120000 + 120000 e^{0.05 t}$.
WolframAlpha says $B(5)=120000 e^{0.25}-120000\approx 34083.1$
The real question is this: If you could have taken a loan and bought a Tesla today for 27,000, how much would the same model cost in 5 years? This is not a question that we want to address here.
File