$1.$ Suppose instead of ensuring you have enough money to last through your lifetime, you decide to spend $$200,000$ per year in retirement. How long until you run out of money?

$2.$ Assume you plan to leave nothing when you pass away, and you can earn a $6\%$ return on your investment.

a$.$ If you start saving for retirement at age $25,$ how much will you need to save each year to meet your savings goal?

b$.$ If you start saving for retirement at age $35,$ how much will you need to save each year to meet your savings goal?