Part D. Answer using Excel preferred. Suppose you are 30. You expect to retire a

ID: 2815853 • Letter: P

Question

Part D.

Answer using Excel preferred.

Suppose you are 30. You expect to retire as soon as you reach age 65, and live to age 100. Your real annual labor income is $150,000 a year until age 65 Suppose the real discount rate is 2%. Suppose from age 40 you start paying social security tax of $12,000 and continue to do so each year until retirement Assume that all cash flows occur in annual frequencies and at year end, and the last social security tax is made when you just turn 65 4. What is your permanent income? How much do you need to save (including both personal and social security savings) each year during your working years in order to maintain a constant level of annual consumption that equals the permanent income? Verify that the PV of savings equal to the PV of consumption in retirement years. How much is your personal savings each year after you start paying social security tax? What is the annual benefit you get from social security after retirement? Does joining social security change your permanent income? Suppose you just won a lottery of $300,000 on your 30th birthday. By how much percent will your permanent income increase? a. b. c. d.

Explanation / Answer

Age of the person=30 Years

Expected to retire at the age of 65 years

Real discount rate =2 percent

Income until the age of 40 =$150000

Tax = $ 12000

Hence this is a Even Cash Flows Problem. And the Cash Flow analysis table is as below

CFAT= $7089750

Excluding taxes you need to save $138000 each year during your working years.

This $138000 includes your Personal savings and Social Security Savings. This is to maintain constant annual consumption that will be equal to the permanent income.

The Cash Flow Analysis table explains PV Savings = PV Consumption.

If you just won a lottery $300000 on your 30th birthday

300000-150000 =$150000

150000/300000*100 = 50 percent

But generally lottery has no impact on the permanent income . it has an imapct when the amount is used for investing in stocks , mutual funds etc.

my personal savings each year after you started paying social security tax $138000.

1 150000 12000 1.02 138000 140760 2 150000 12000 1.04 138000 143520 3 150000 12000 1.062 138000 146556 4 150000 12000 1.084 138000 149592 5 150000 12000 1.106 138000 152628 6 150000 12000 1.128 138000 155664 7 150000 12000 1.151 138000 158838 8 150000 12000 1.175 138000 162150 9 150000 12000 1.199 138000 165462 10 150000 12000 1.223 138000 168774 11 150000 12000 1.248 138000 172224 12 150000 12000 1.274 138000 175812 13 150000 12000 1.3 138000 179400 14 150000 12000 1.326 138000 182988 15 150000 12000 1.353 138000 186714 16 150000 12000 1.381 138000 190578 17 150000 12000 1.409 138000 194442 18 150000 12000 1.438 138000 198444 19 150000 12000 1.467 138000 202446 20 150000 12000 1.497 138000 206586 21 150000 12000 1.528 138000 210864 22 150000 12000 1.559 138000 215142 23 150000 12000 1.591 138000 219558 24 150000 12000 1.623 138000 223974 25 150000 12000 1.657 138000 228666 26 150000 12000 1.69 138000 233220 27 150000 12000 1.725 138000 238050 28 150000 12000 1.76 138000 242880 29 150000 12000 1.796 138000 247848 30 150000 12000 1.833 138000 252954 31 150000 12000 1.87 138000 258060 32 150000 12000 1.908 138000 263304 33 150000 12000 1.947 138000 268686 34 150000 12000 1.987 138000 274206 35 150000 12000 2.02 138000 278760 7089750