Ella Funt would like to set up her retirement account that will begin in 30 years. To play it safe, she wants to assume that she will live forever and she will withdraw $120,000 annually. Assuming her account will earn 9% interest during the next 30 years and 6% interest afterwards forever, how much will Ella need to save annually over the next 30 years to fund her retirement account?

First, we need to determine the present value of her investment at the retirement point. We will use the following formula for a perpetual annuity:

FV= Cf/i

FV= 120,000/0.06= $2,000,000

Now, we can calculate the annual deposit required to reach the objective:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= [2,000,000*0.09) / [(1.09^30) - 1]

A= $14,672.70

andromache andromache · Answer 2 · 2022-03-01T13:07:45+01:00

The amount that Ella need to save annually over the next 30 years to fund her retirement account is $14,672.70

Calculation of the annual deposit:

First the future value is

= Withdraw amount / rate of interest

= 120,000/0.06

= $2,000,000

Now the annual deposit is

FV= {Annual deposit *[(1+interest rate)^number of years-1]}/interest rate

So,

A= [2,000,000*0.09) / [(1.09^30) - 1]

A= $14,672.70

Hence, we can conclude that The amount that Ella need to save annually over the next 30 years to fund her retirement account is $14,672.70

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