Question

Today is your 25^th birthday.  You have decided that it is necessary to plan your own retirement since you are not confident that government benefits will be available when you retire.  You will make annual payments into an account earning 5% APY starting on your next birthday (26^th) a year from now.  Your last payment will occur on your 70^th birthday.  You have decided that you need to plan for payments of $500,000 per year and that there will be a total of 20 yearly payments made starting on your 70^th birthday.  

1. How much should be in your account on your 70^th birthday in order to accomplish your goal?
2. How much will your annual payment until you retire need to be in order to accomplish your goal?
3. Suppose this is your 45^th birthday, instead of your 25^th birthday in the problem above.   Now, how much will your annual payment until you retire need to be in order to accomplish your goal?

Answer 1

A.Amount required on 70th birthday = Present value of all amount required in future

= 500,000 + 500,000*PVAF*(5%, 19 periods)

= 500,000 + 500,000*12.085

= $6,542,500

B.Future value of Annuity = Annual amount*[((1+r)^n - 1}/r]

Let annual payment be x

6,542,500 = x*[{(1.05)^45 - 1}/0.05]

6,542,500 = 159.7001558x

x = $40,967.40

Hence, annual payment required = $40,967.40

C. Let annual payment be x

6,542,500 = x*[{(1.05)^25 - 1}/0.05]

6,542,500 = 47.7270988x

x = $137,081.45

hence, annual payment will be $137,081.45