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%. Unfortunately, his income oscillates periodically so his yearly saving rate at time $t$
is in fact $6000(1+\cos t)$. That is, it was 1000 a month initially, but dropped to about 500 per month nine months later, and hit a rock bottom of 0 in about 3.1415926 years later. (But then it re-bounced afterwards with 500 per month in about 4.71 years). Determine the price of the car he can purchase.
Put your answer into DE-Poll using two decimals
The answer is about 28,643.2
Hint We want to solve
$B'=.05 B+6000(1+\cos t)$ with the initial condition $B(0)=0$, and determine the value of $B(5)$.