At your age (assume 20) you can assume that you will live to be 100. If you grad
ID: 2757372 • Letter: A
Question
At your age (assume 20) you can assume that you will live to be 100. If you graduate at 23 and start to work, you can expect to work for 47 years, until age 70. At that time you will be eligible for full Social Security benefits, which can reasonably be expected to be $3,000 per month, and which will be received monthly for the rest of your life. You can reasonably expect that your retirement savings will earn an average of 8 percent per year throughout the period that you accumulate your retirement funding and during your retirement years. Further assume that you will want to have an annual income of $120,000 throughout your retirement.
1. Ignoring inflation in all calculations, how much will you need to have saved at retirement in order to be able to fund your retirement?
2. How much will you have to save each year in order to fund this amount if you start at 23?
3. How much will you have to save each year in order to fund this amount if you start at 25?
4. How much will you have to save each year in order to fund this amount if you start at 30?
5. How much will you have to save each year in order to fund this amount if you start at 40?
6. Briefly explain how you think those funds should be managed. That is, suggest a reasonable overall plan to achieve your goal, using all of the tools we have considered throughout the course.
Explanation / Answer
Social security is received $3000 per month from 71st Year to 100th Year. We need to know what is the value of this annuity fund at the end of 70th Year. Here A=3000 , i=8/12=0.666% , n=30*12=360 Present Value of an annuity=PV= A*[ (1+r)^n -1]/[(1+r)^n * r] PV=3000*(1.00666^360-1)/((1.00666^360)*(0.00666)) [say A] 409161.4 He needs $120000 from 71st Year till 100th Year as annual income Here A=120000 , i=8 , n=30 PV=120000*(1.08^30-1)/((1.08^30)*(0.08)) [say B] 1350934 (1)So his contribution to retirement fund should be [B-A] at end of 70th year=1350934-409161.4 [C] 941772.6 (2)The amount [C] is the future value of all contribution made by him during his working period. Let the annual contribution be A Compound Value of an annuity=FV=A*[ (1+r)^n - 1)]/r , n=47,r=8 941772.6=A*(1.08^47-1)/0.08 or A=941772.6*0.08/(1.08^47-1) 2079.43 (3) Here , n=70-25=45 or A=941772.6*0.08/(1.08^45-1) 2436.63 (4) Here , n=70-30=40 or A=941772.6*0.08/(1.08^40-1) 3635.39 (5) Here , n=70-40=30 or A=941772.6*0.08/(1.08^30-1) 8313.43 (6) The contribution to pension fund should start at 23 to have less annual burden as every year of delay increases the annual contribution needed.
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