Assume that you are $30$ years old today and that you are planning on retirement at age $70.$ Your

current salary is $$75,000$ and you expect your salary to increase at a rate of $4\%$ per year as long as you work. To

save for your retirement, you plan on making annual contributions $($on your birthday$)$ to a retirement account. Your

first contribution will be made on your $31$st birthday and will be $10\%$ of this year's salary. Likewise, you expect to

deposit $10\%$ of your salary each year until you reach age $70.$ Assume that the rate of interest is $7\%.$

a$.$ What is the present value $($today$)$ of your planned retirement savings?

b$.$ What is the future value of your retirement savings when you retire $40$ years from today at age $70?$

c$.$ At retirement $($age $70)$ you will begin withdrawing equal annual payments to pay for your living expenses during

retirement $($on your $70$th birthday$).$ If you expect to die one day before your $101$st birthday $($your last withdrawal

will be on your $100$th birthday, your $31$st withdrawal$)$ and if the annual rate of return is $7\%,$ then how much money

will you withdraw in each of your years of retirement?

d$.$ Suppose that you wish to be able to withdraw $$200,000$ per year at the beginning of each year, for how many

retirement years can you withdraw $$200,000?$