Suppose you want to start saving for retirement. You decide to continuously invest $15000 of your income each year in a risk-free investment with a 3% yearly interest rate, compounded continuously.

If $y$ is the value of the investment, and $t$ is in years:
$\frac{dy}{dt} =$
Your answer should be in terms of $y$.

You start investing at $t=0$ so $y(0)=0$.
$y(t) =$

What is the size of your investment after 20 years.
$y(20) =$