You believe that if you retired today, you would need a portfolio value of $$1,500,000.$ However, you plan to retire in $35$ years and you think the cost of living $($living expenses$)$ will increase by $3\%$ per year.

a$.$ What is the portiolio value needed in $35$ years if you want to retire at the same standard of living?

b$.$ Based on the amount in part a$,$ how much do you have to invest annually at a rate of $7\%$ to reach your retirement goal?