Suppose you are 30. You expect to retire as soon as you reach age 60, and live to age 100. Your real annual labor income is $80,000 a year until age 60. Suppose the real discount rate is 3%. Ignore taxes and social security. Assume that all cash flows occur at year end.

a. What is your permanent income? How much do you need to save each year in order to maintain a constant level of annual consumption that equals the permanent income?

b. Suppose you just won a lottery of $300,000 on your 30th birthday. By how much will your permanent income increase?

Please show all work and calculations, thanks!