Question

You are 25 years old and plan to retire 35 year from today. You expect that you will live 30 years after retiring. You want to have enough money upon reaching retirement age to withdraw $150,000 from the account at the beginning of each year you expect to live, and yet still have $1,000,000 left in the account at the time of your expected death (65 years from now). You plan to accumulate the retirement fund by making equal annual deposits at the end of each year for the next 35 years. You expect that you will be able to earn 12% per year on your deposits. However, you only expect to earn 6% per year on your investment after you retire since you will choose to place the money in less risky investments. What equal annual deposits must you make each year to reach your retirement goal?

Answer 1

I have mentioned all known data in following time line :

To get equal installments we need to understand how much money is required at the end of 60 years . to calculate that I will use Excel .

To calculate present value at the end of year 60 of annuity payments of $150000 for 30 years at the beginning of the year and $100000 in account

Use excel function as follows

This will give us PV = $2362718.28

To calculate installments we need to make sure after 35 years we have $2362718.28 amount , thus it become Future value FV = $2362718.28.

Using excel formula as show below we get following result:

Thus we get annual installment as $ 5473 .

Note : Kindly ignore the currency sign.