Your retirement account has a fixed rate of 8% per year paid yearly. You start saving for retirement at age 30 with a target retirement age of 65 and $0 in your savings account. Set up and solve a suitable first order differential equation to answer the following questions (compute all interests and payment on a yearly basis).
1. Suppose you set aside $500 every month. How much will you have for your retirement?
2. You want to retire with $500,000. How much should you save every month?
3. Assuming that your salary is going to increase 5% per year during your lifetime you can also decide your contribution should follow suit your monthly contribution increase by 5% every year. If your starting contribution is $500 every month, how much money will you have saved at retirement age?
4. Assuming again that your contribution is increasing by 5% every year, what should your starting contribution be if you want reaching $500,000 by retirement age?