4. Suppose you are 30. You expect to retire as soon as you reach age 65, and liv
ID: 2815847 • Letter: 4
Question
4. 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. 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? a.Explanation / Answer
A. Permanent Incomne is the Real Annual Labor Income which is $150,000. So apparently, we have to maintain a constant level of annual consumption that equals to $150,000 which means you need $150,000 every year to sustain. Also, $12000 is an expense which would be paid out of the income but still our permanent income will be the income which we have recieved in a year.
Follow the steps:
1. Open Excel and type =FV
2. Now we are going to calculate the value of $150,000/p.a. at 2% from 66th to 100th year. I have assumed that compounding rate is same as discount rate which is 2%. So enter, RATE= 2%, NPER= 35, PMT=-$150,000, TYPE=0 (since cash flow occurs at end). You'll get $7,499,172 which is the value of $150,000/p.a. at 2% after 35 years.
3. Now we'll discount $7,499,172 to 35 years as we want to know the value of those $150,000/p.a. on retirement. So type =PV. Then Enter, RATE= 2%, NPER=35, F.V.= 7,499,172, TYPE=0. You'll get $3749793. Now this is the amount you require at retirement in order to recieve $150,000 annualy till 100th year.
4. Now we need to know how much you have to save from 30th year onwards to reach at $3749793. So type, =PMT. Then Enter, RATE 2%, NPER=35, F.V.= $3749793 & TYPE=0. You'll get $75004.
$75004 is the amount you have to save annualy to maintain a constant level of annual consumption that equals to permanent income.
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