Question

Debbie has $223,188.4 accumulated in a 401K plan. The fund is earning a low, but safe, 3% per year. The withdrawals will take place annually starting today. How soon will the fund be exhausted if Debbie withdraws $40,000 each year?

Answer 1

6.20 years

Step-by-step explanation:

Use Followingformula to calculate the time period to exhaust the fund

PV of Annuity = Annuity Payment X ( 1 - ( 1 + interest rate )^-n ) / interest rate

Where

PV of Annuity = $223,188.4

Annuity payment = $40,000

Interest rate = 3%

$223,188.4 = $40,000 X ( 1 - ( 1 + 3% )^-n ) / 3%

$223,188.4 / $40,000 = ( 1 - ( 1 + 3% )^-n ) / 3%

5.57971 = ( 1 - ( 1 + 3% )^-n ) / 3%

5.57971 X 3% = ( 1 - ( 1 + 3% )^-n )

0.1673913 = ( 1 - ( 1 + 3% )^-n )

1 / 1.03^n = 1 - 0.1673913

1 / 1.03^n = 0.8326087

1.03^n = 1 / 0.8326087

1.03^n = 1.2010

n log 1.03 = log 1.2010

n = log 1.2010 / log 1.03

n = 6.20 years