Question

You are 25 years old, having just started working. You are considering a retirement plan for a retirement at the age of 65. You want to be able to withdraw $76,000 from your savings account on each birthday for 20 years following your retirement at the age of 65. Your first withdrawal will be on your 66th birthday. To achieve your goal, you intend to make equal annual deposits in a pension scheme which offers 7% interest per year. According to the Investment A, you expect a lump sum of $ 100,000 from a family inheritance fund that you will receive on your 50th birthday. You will put this fund into the retirement savings account. Furthermore, you have invested in a portfolio what will be giving you $ 1,600 per year (from age 25 through age 65) which are to be added the retirement savings account as well. If you begin making these deposits on your 25nd birthday and continue to make deposits until you are 65 (your last deposit will be made on your 65th birthday), what is the amount you are required to deposit annually to be able to make the desired withdrawals at retirement? Investment B Here you still have the same retirement plan in mind, in other words you want to be able to withdraw $76,000 from your savings account on each birthday for 20 years following your retirement at the age of 65. However, the investment criteria are different: You have invested in a business which gives an annual net profit of $ 2,600 per year. Furthermore, your employer will contribute $ 700 to the account per year as part of the company’s profit-sharing plan starting from age 45 to 65. What amount must you deposit annually now to be able to make the desired withdrawals at retirement? Which investment will you choose and why

Answer 1

Investment A,

let's create timeline first

current age 25years------------------------retirement age 65 years---------------------- die at 85 year

period in which we need to contribute = 65 to 25 = 41 years ( we consider both 65 and 25 Birthday so)

Retirement period in which we need $76000 per year = 66 to 655= 25 years

Now find the present value at the End of 65

the rate of return is 7%

here use excel formula.

present value = =pv(rate,nper,pmt,fv,type)

=pv(0.07,20,76000,0,0)

= $805145.08

where pv = present value at end of 65th year

nper = no of year in retirement

pmt = yearly expenses need in retirement years

fv = future value

type = 0= ending because we need end of every year

Following investment made.

inestment 1

Investment value at the end of 65th year

expect a lump sum of $ 100,000 from a family inheritance fund at the beginning of 50th birthday

Future value of Investment at the end of 65th year

Future value = =fv(rate,nper,pmt,pv,type)

=pv(0.07,16,0,100000,0)

= $295216.37

where fv = Future value at end of 65t

nper = no of year in retirement = 50 to 65 year

pmt = 0

pv = Present value

invetment 2

invested in a portfolio what will be giving you $ 1,600 per year (from age 25 through age 65)

Future value of Investment at the end of 65th year

Future value = =fv(rate,nper,pmt,pv,type)

=pv(0.07,41,1600,0,0)

= $39335.99

Total invetment value at the end of 65th year = $39335.99 + $295216.37 = $334552.36

Amount will need at the end of 65th year = Present value of exp in retirement - Future value of investment = $805145.08 - $334552.36 = $470592.71

Now above value will be the future value at 65 years.

now find pmt (year contribution)

yearly contribution (PMT) = =pmt(rate,nper,pv,fv,type)

=pmt(0.07,41,0,$470592.71,0)

= $2192.79

where,

pv = 0

nper = no of year up to retirement

pmt = Annual contribution

fv = future value

type = 0= ending because we need end of every year

hence I need to contribute $2192.79 every year to fund retirement in invetment A.

Investment B

We need the same Present value of $805145.08 but Investment will be different.

Investment 1

Annual business profit of $2600 For 41 years

Future value of Investment at the end of 65th year

Future value = =fv(rate,nper,pmt,pv,type)

=pv(0.07,41,2600,0,0)

= $557984.88

Investment 2

employer will contribute $ 700 to the account per year as part of the company’s profit-sharing plan starting from age 45 to 65 for 21years.

Future value of Investment at the end of 65th year

Future value = =fv(rate,nper,pmt,pv,type)

=pv(0.07,21,700,0,0)

= $31405.62

Total invetment value at the end of 65th year = $31405.62 + $557984.88 = $589390.50

Amount will need at the end of 65th year = Present value of exp in retirement - Future value of investment = $805145.08 - $589390.50 = $215754.58

Now above value will be the future value at 65 years.

now find pmt (year contribution)

yearly contribution (PMT) = =pmt(rate,nper,pv,fv,type)

=pmt(0.07,41,0,$215754.58,0)

= $1005.33

where,

pv = 0

nper = no of year up to retirement

pmt = Annual contribution

fv = future value

type = 0= ending because we need end of every year

hence I need to contribute $1005.335every year to fund retirement in invetment B.

We must choose Investment B

Because the Future value of investment is higher so we need to contribute 1005.335 that is lower than Investment A. Even less than half.