Question

You plan to retire in 19 years. At the point of retirement, you want to be able to withdraw 32,877 at the end of each year forever. Assume that you earn a 7.29% rate of return prior to retirement and an 5.02% rate of return after retirement. If you do not want to make any further contributions to your retirement fund, how much do you need today? Round answer to the nearest dollar.

Answer 1

Since no any further contributions will be made to the retirement fund, the amount you need today is $172,014.

Calculation of Present Value and Present Value of a Perpetuity

The first step is to calculate the present value (PV) of the contribution at the point of retirement in 19 years using the formula for calculating the present value (PV) of perpetuity as follows:

PV in 19 years = CF / R ............................................. (1)

Where;

PV in 19 years = Present value (PV) of the contribution at the point of retirement in 19 years = ?

CF = Cash flow or yearly expected withdrawal = $32,877

R = Rate of return after retirement = 5.02%, or 0.0502

Substituting the values into equation (1), we have:

PV in 19 years = $32,877 / 0.0502 = $654,920.3187251

The amount you need today can be calculated using the present value formula as follows:

PV = FV / (1 + r)^n ……………………………………………. (2)

Where;

PV = Present value or the amount you need today = ?

FV = Future value or PV in 19 years = $654,920.3187251

r = rate of return prior to retirement = 7.29%, or 0.0729

n = number of years = 19

Substituting the values into equation (2), we have:

PV = $654,920.3187251 / (1 + 0.0729)^19 = $654,920.3187251 / 3.80737505803714 =  $172,013.607470218

Rounding to the nearest dollar, we have:

PV = $172,014

Therefore, the amount you need today is $172,014.

Learn more about present value here: brainly.com/question/17322936.