Question

Tom has a self-managed retirement plan through her company and would like to retire in 10 years and wonders if her current and future planned savings will provide adequate future retirement income. Here are her goals and other relevant information:

• Tom wants a 25-year retirement annuity that begins 11 years from now (end of year 11) with a constant annual payment equal to $50,000 in today’s dollars adjusted for 2 % inflation over the 11-year period.

• Tom currently has $200,000 in her retirement account. She expects these savings and any future deposits into her retirement account to earn 7% compounded annually. Also, she expects to earn the same 7% after she retires.

  Answer the following questions to help Tom finalize her retirement planning.

1. What is Tom desired annual retirement income in the first year of retirement, i.e. her retirement income 11 years from today (end of year 11)?

2. Assuming that inflation is zero from year 11 onward, how much will Tom need 10 years from today (end of year 10) to fund her desired retirement annuity (please note that annuity payments start from the end of year 11)?

3. Assume that inflation is zero from year 11 onward. In addition to the $200,000 balance today, Tom will fund her future retirement goal from question (b) by making 10 annual equal deposits at 7% compounded annually into her retirement account starting a year from today (the last deposit will be made when Tom retires at the end of year 10). How large does this annual deposit need to be in addition to the initial $200,000 invested in Tom retirement fund?

4. Assume that inflation is 2% during the entire period, even after retirement. Tom is worried about her purchasing power eroding during retirement. She would like her first retirement withdrawal to be equal to the amount you found in question (a), and then to increase by 2% annually over the remaining 24 withdrawals. How much will Tom need now at retirement given her 7% expected rate of return?

5. In addition to the $200,000 balance today, Tom will fund her adjusted future retirement goal from question (d) by making 10 annual equal deposits at 7% compounded annually into her retirement account starting a year from today (the last deposit will be made when Tom retires). How large does this annual deposit need to be in addition to the initial $200,000 invested in Tom retirement fund?

Answer 1

Answer :

Given Data :

Tom has a self-managed retirement plan through her company and would like to retire in 10 years and wonders if her current and future planned savings will provide adequate future retirement income. Here are her goals and other relevant information:

• Tom wants a 25-year retirement annuity that begins 11 years from now (end of year 11) with a constant annual payment equal to $50,000 in today’s dollars adjusted for 2 % inflation over the 11-year period.

• Tom currently has $200,000 in her retirement account. She expects these savings and any future deposits into her retirement account to earn 7% compounded annually. Also, she expects to earn the same 7% after she retires.

a. What is Tom desired annual retirement income in the first year of retirement, i.e. her retirement income 11 years from today (end of year 11)?

As inflation is 2% over 11 years and she wants constant annual payment equal to $50,000 in today’s dollars

Here, we should understand that if we have $1 amount today and inflation is 2 % then after end of the one year we have to pay $ 1.02 for the thing purchased as we buy it from $ 1 . It is due to Inflation.

Hence,Tom's desired annual retirement income in the first year of retirement, i.e. her retirement income 11 years from today (end of year 11) be = $ 50000 x Annuity factor at 2 % for 11 years = $ 50,000 x (1.02)¹¹ = $ 50,000 x 1.2434 = $ 62170

b. Assuming that inflation is zero from year 11 onward, how much will Tom need 10 years from today (end of year 10) to fund her desired retirement annuity (please note that annuity payments start from the end of year 11)?

As there is Zero inflation,hence it is not needed to adjust desired rate of return which is 7%  

Tom need 10 years from today (end of year 10) to fund her desired retirement annuity be = $ 50,000 / (0.07) =

$ 714,285.71 /-

c. Assume that inflation is zero from year 11 onward. In addition to the $200,000 balance today, Tom will fund her future retirement goal from question (b) by making 10 annual equal deposits at 7% compounded annually into her retirement account starting a year from today (the last deposit will be made when Tom retires at the end of year 10). How large does this annual deposit need to be in addition to the initial $200,000 invested in Tom retirement fund?

= Amount needed to invested = Amount required at end of 10 the year to get desired return from 11 the year - Invested after 10th year with interest = $ 714,285.71 - ( $ 200000 x ( 1.07)¹⁰) = $ 714,285.71 - $ 393,430.27

= $ 320,855.44

d. Assume that inflation is 2% during the entire period, even after retirement. Tom is worried about her purchasing power eroding during retirement. She would like her first retirement withdrawal to be equal to the amount you found in question (a), and then to increase by 2% annually over the remaining 24 withdrawals. How much will Tom need now at retirement given her 7% expected rate of return?

Step 1 : Calculation of Expected Rate of Return

As there is 2 % inflation for 11 years and Tom expects the rate of return as 7% on investment. Hence such real time rate of return should be get effected by the inflation. As purchasing power is decreased by inflation

Hence, Expected Rate of Return = r - ( r x I ) =  7 % - ( 7% x 2% ) = 7% - 0.14% = 6.86%

Here, r = Real/ expected rate of return

I = Inflation Rate

Step 2 : Tom need to invest now so at retirement given her 7% expected rate of return with effect of inflation at 2% by not affecting Purchasing power be :

= $ 62170 / 6.86% = $ 906268.22 /-

e. In addition to the $200,000 balance today, Tom will fund her adjusted future retirement goal from question (d) by making 10 annual equal deposits at 7% compounded annually into her retirement account starting a year from today (the last deposit will be made when Tom retires). How large does this annual deposit need to be in addition to the initial $200,000 invested in Tom retirement fund?

= $ 906268.22 - ( $ 200000 x ( 1.07)¹⁰)  

= $ 906268.22 - $ 393,430.27

= $ 512,837.95