Question

Roth IRA Worksheet Lainey Wilkinson is a 36 years old individual who works at a local library. She starts to invest $3,000 per year this year in a “Roth IRA”. For investments in a Roth IRA, you will never pay taxes on the interest/dividends/profits. Assume that her investments will make 8% annually until her retirement. I. How much will be there in Lainey’s IRA account when she retires at 66. II. Assuming that Roth IRA makes 7% annual return after retirement and she can make annual withdrawal, how much will she be able to withdraw per year if she plans to withdraw all the fund from Roth IRA in a) 15 years, b) 20 years, and c) 25 years. Use the attached worksheet 2.

Answer 1

Roth IRA after 30 years to her retirement with an annual installment of $3000 per year will give a value of

annual investment	3000
return	0.08
retires at 66 - her age now
66-36 =    30
time	30
fva = annuity( ((1+i)^n-1)/i)
=$339849.6333

b . Future value of annuity after 30 years of now =  $339849.6333

if she plans to withdraw the fund in 15 years what is the annuity if rate of interest changed to 7%.

per year withdrawl or annuity would be :
time   15
  
pva = annuity* ((1+i)^n-1)/i*(1+i)^n  
339849.6 = annuity *69.33176431  
annuity =339849.6/69.3318
4901.788332   annuity
so he will receive 4901 .78 annually for 15 years   
  

c if after 20 years of retirement
pva = annuity* ((1+i)^n-1)/i*(1+i)^n  
339849.6=annuity*(158.6396197)
annuity = 339849.6/158.6396197
annuity =

2142.274635

d. 25 years
pva = annuity* ((1+i)^n-1)/i*(1+i)^n
339849.6=annuity *343.279891
annuity =

990.0074007

so after retirement every year she will recieve &990.007 for 25 years