Question

You plan on retiring in 40 years at age 65.  You currently have $20,000 (graduation present) that you are going to deposit today in a bond that will yield 10% a year for the entire 40 years (traditional IRA).  At age 40 you will receive an inheritance from your parents of approximately $20,000 which you will invest in mutual funds that will yield 9% a year for 25 years (Traditional IRA).  The current discount rate is 5.5%, the risk-free rate is 3% and if we were using beta it would be 1.2.  The humidity in Austin averages around 95 degrees during the summer.  You also figure that if Prof. Elliott, (2 t’s) can live to 90 you can make it to 95.  So at age 65 you decide to purchase an annuity type investment, with the interest rate being 3.0% (according to Tony Robbins).  You want to receive $120,000, gross, a year from age 65 to 95, (30 years) and then you will pass on to the great beyond.  (you will also receive $15,000 a year from Social Security, which will be handled for tax purposes the same as a Traditional IRA, which means this is part of the $120,000 gross). Do you have enough money from the two investments mentioned in the first part of this problem to fund your retirement, if not then….. a)With this in mind, how much must you deposit a year for 40 years, (25 to 65), at 10% in a Roth IRA, (mutual funds), ignoring inflation to achieve your retirement goals?  b) How much will you net if you are in the 30% federal tax bracket each year?

a) How much a year from 25 to 65 must be deposited to achieve this goal?  Round to the nearest cent

b) How much will you net each year if when you retire you are in the 30% tax bracket?   Round to the nearest dollar.

Answer 1

--> Current age = 25 years

--> To retire in 40 years at the age of 65.

- Capital available at the age of 25 = $20,000
Return expected = 10% per annum
Compounded amount after 40 years = $ 905,185

- Capital available at the age of 40 = $20,000
Return expected = 9% per annum
Compounded amount after 25 years = $ 172,461

--> Total capital available at the age of 65 is 905,185 + 172,461 = $1,077,646
This sum of money, when invested at the rate of 3% during the retirement period (65-95 years) against an annuity plan so as to get $105,000 (120,000 - 15,000) every year, would not suffice. This sum of money would get exhausted in approximately 12.5 years.

a) The total amount of capital that the investor needs to have at the beginning of his retirement is $2,058,046. (calculated by discounting the PMT of 105,000 at 3% for 30 years and deriving the present value).
The amount of sum required each year for investment at 10% per annum during the age of 25-65 years is $4,650.
(calculated by considering the future value of 2,058,046 discounted for 40 years at 10% and deriving the PMT).

b) Net income can be calculated in 2 stages -
I) Household income treatment at 30%.
- $105,000 - 30% = $73,500
ii) Social security treatment at 7.65% (social security + medicare)
- $15,000 - 7.65% = $13,853

Therefore, total net income = 73,500 + 13,853 = $87,353