Question

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 $160,000 annually. Assuming her account will earn 10% interest during the next 30 years and 5% interest afterwards forever, how much will Ella need to save annually over the next 30 years to fund her retirement account?

Answer 1

Answer:

During retirement period:

Rate of interest = 5%

Annual withdrawal forever = $160,000

Retirement corpus required = 160000 / 5% = $3,200,000

As the question does not say whether annual withdrawal will be at the end of year or beginning of year, two answers are given:

Assuming annual withdrawal during retirement is at the end of year:

Retirement fund required at the beginning of 31st year = $3,200,000

For saving:

Time period = 30 years

Interest rate = 10%

Annual deposit required = PMT (rate, nper, pv, fv, type) =PMT (10%, 30, 0, -3200000,0) = $19453.59

Ella need to save annually over the next 30 years = $19453.59

Assuming during retirement annual withdrawal is at the beginning of year:

Retirement fund required at the beginning of 31st year = $3,200,000 + $160,000 = $3,360,000

Annual deposit required = PMT (rate, nper, pv, fv, type) =PMT (10%, 30, 0, -3360000,0) = $20426.27

Ella need to save annually over the next 30 years = $20,426.27