Question

You are 40 years old and want to retire at age 65. Each​ year, starting one year from​ now, you will deposit an equal amount into an investment account that pays 4% interest. The last deposit will be on your 65th birthday. On your 65th birthday, you will switch the accumulated savings into a safer bank account that pays only 4.2​% interest. You will withdraw your annual income of $110,000 at the end of that year​ (on your 66th ​birthday) and each subsequent year until your 90th birthday. On that birthday you want to give  ​$250,000 to your children. How much do you have to save each year to make this retirement plan​ happen?  

How much do you have to save per year during your working years in order to achieve your retirement​ goal?

Answer 1

- You will make periodic withdrawal of $110,000 each year for 25 years from 66th birthday to 90th birthday. You will also left $250,000 on your 90Th birthday to give to your children

Calculating its Present Value at age 65:-

Where, C= Periodic Payments = $110,000

r = Periodic Interest rate = 4.2%

n= no of periods = 25 years

P = Last payment to be left = $250,000

Present value = $1,682,671.30 + $89,381.38

Present value = $1,772,052.68

So, the amount you have to accumulate at retirement age is $1,772,052.68

Now, Calculating the Periodic amount needs to be save to accumulate the retirement amount:-

Where, C= Periodic Deposits

r = Periodic Interest rate = 4%

n= no of periods = 25 years  

C = $42,550.46

So, the amount you have to save per year during your working years in order to achieve your retirement​ goal is $42,550.46

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