Question

QUESTION 10 Assume that you have 40 years until retirement and have just started your first job. Once you retire, you anticipate that you will live for 30 additional years. Assume that you will require $100,000 per year to support yourself in retirement. All investments that you make will go into and stay in an account that returns 0.046 per year (i.e. however much you have at retirement will sit in that account and continue to accrue interest on the remaining balance.) How much will you have to save each year over the next 40 years to meet your goal? Assume that your first investment occurs at the end of your first year of work fyr 1) and that the last of your 40 investments occurs on the last day that you are employed fyr 40). For simplicity, assume that your first withdrawal is at the end of your first retirement year yr 41).

Answer 1

The first step is to find the size of the retirement fund that allows you to withdraw $ 100,000 per year for 30 years of your retirement. The size of the fund is found using present value of annuity equation

Size of retirement fund = $100,000 x [(1 + 0.046) 30-1] 0.046 x (1 +0.046) 30

Size of the retirement fund =  $1,609,896.77

Thus in 40 years, you must have $1,609,896.77 in the retirement account to make annual withdrawals of $ 100,000 per year.

The amount must that must be saved each year to reach the goal is found using future value of annutiy equation.

$1,609,896.77 Ax [(1 +0.046) 40-1] 0.046 =

Solving for A in the above equation

A =  $14,684.16 $\approx$   $ 14684

The amount that must be saved each year = $ 14684