Debbie has $717,683 accumulated in a 401K plan. The fund is earning a low, but safe,...
Debbie has $717,683 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 $70,000 each year?
Homework Answers
Present value of annuity due=(1+rate)*Annuity[1-(1+interest rate)^-time period]/rate
717,683=1.03*70,000[1-(1.03)^-time period]/0.03
717,683=2,403,333.33[1-(1.03)^-time period]
[1-(1.03)^-time period]=(717,683/2,403,333.33)
1-(717,683/2,403,333.33)=(1.03)^-time period
0.701380166=(1/1.03)^time period
Taking log on both sides;
log 0.701380166=time period*log (1/1.03)
time period=log 0.701380166/log (1/1.03)
=12 years(Approx).
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