Please show and explain all work in text as clear as possible.

You believe you will need to have saved $500,000 by the time you retire in 40 years. If the interest rate is 4% per year, how much must you save each year until retirement to meet your retirement goal?

b) A couple thinking about retirement decides to put aside $3,000 each year in a savings plan that earns 8% interest. In 5 years, they will receive a gift of $10,000 that also can be invested. How much money will they have accumulated 30 years from now?

c) If the couple in (b) has a goal to retire with $800,000 of savings, how much extra do they need to save every year?