You will retire in 40 years. At that time you will begin making annual withdrawals and...

You will retire in 40 years. At that time you will begin making annual withdrawals and the first withdrawal will need to have the purchasing power that $127,849 has today. You will withdraw the same amount of money each year of retirement (and you recognize that its purchasing power will fall as inflation continues). You plan to live for 24 years during retirement, necessitating 24 withdrawals. Inflation equals 6% per year. Obviously, you will need to save (and invest) money to generate the nest egg that will be spent during retirement. The "fund" you plan to invest in earns 9% per year until retirement, and then during retirement, it earns 3% per year. How much must you save each year (with payments into your retirement savings vehicle beginning one year from today), in order to meet your retirement needs?

Expert Solution

Amount of first withdrawal= A*(1+i)^n

Where

A= equivalent amount today (given as $127,849), i= Inflation rate (given as 6%) and n= time till retirement (40 years)

Plugging the inputs,

Amount of first withdrawal= $127,849*(1+6%)^40 = $1,315,018.75

Nest egg is the present value of annuity due comprising 24 payments in retirement with interest at 3%, ascertained at $22,938,672.14 as follows:

Amount to be saved each year (ordinary annuity for 40 years, at 9% interest)= $67,889.51

Calculated as follows:

jeff jeffy answered 2 years ago

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