Your father's employer was just acquired,and he was given a severance payment of $305,000,which he invested at a 7.5% annual rate.He now plans to retire,and he wants to withdraw $35,000 at the end of each year,starting at the end of this year.How many years will it take to exhaust his funds,i.e. ,run the account down to zero?
A) 10.99
B) 13.49
C) 16.27
D) 11.73
E) 14.66

Question

Quizplus · Accepted Answer

This is a problem that involves the concept of the time value of money, specifically an annuity where a fixed amount is withdrawn each year. The formula to calculate the number of periods (n) for an annuity is:$$ n = \frac{\log(\frac{PMT}{PMT - r \times PV})}{\log(1 + r)} $$Where:- PMT = annual withdrawal amount ($35,000)- r = annual interest rate (7.5% or 0.075)- PV = present value of the investment ($305,000)Plugging in the values:$$ n = \frac{\log(\frac{35000}{35000 - 0.075 \times 305000})}{\log(1 + 0.075)} $$$$ n \approx 14.66 $$Therefore, it will take approximately 14.66 years to exhaust the funds.

Your Father's Employer Was Just Acquired,and He Was Given a Severance