Since no any further contributions will be made to the retirement fund, the amount you need today is $172,014.
<h3>Calculation of Present Value and Present Value of a Perpetuity</h3>
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.
= New Forecast
= Previous period's forecast.
= Smoothing Constant
= Previous period's Actual Demand.