Question

Imagine you are 25 years old right now. You would like to retire in 40 years (at age 65). You would like to fund your retirement. You would like to have enough saving to withdraw $50,000 each year in retirement and you want to plan for 20 hears (the last withdrawal is at age 85).

You will earn 7% annually on your saving before you retire. Then once you retire, you will move your nest egg into a safer investment, earning a 3% annual rate of return.

Assume all payments are made at the end of each year (these are all ordinary annuities).

a) How much do you need to have in your nest egg the day you retire (what is the saving goal)?

b) If you wanted to fund your retirement with one lump sum now (at age 25), how much would you have to invest?

c) Instead of investing one large sum today, what would your annual payments have to be for the next 40 years to reach the retirement goal?

Answer 1

a

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 50000*((1-(1+ 3/100)^-20)/(3/100))

PV = 743873.74

b

Future value = present value*(1+ rate)^time

743873.74 = Present value*(1+0.07)^40

Present value = 49676.17

c

FVOrdinary Annuity = C*(((1 + i )^n -1)/i)

C = Cash flow per period

i = interest rate

n = number of payments

743873.74= Cash Flow*(((1+ 7/100)^40-1)/(7/100))

Cash Flow = 3726.17