Question

_{Your plan is to retire in 50 years. At that point you will be 70 years old. You expect to live until you are 90. If your wealth at age 50 is $400,000 what is the maximum you can spend each year so that when you are 90 your wealth is 50,000. Assume that your wealth will earn 6% per year between your age 70 and age of 90.}

_{The answer is between $36,000 and $37,000 per year. True or False.}

Answer 1

Investment in fund at age 50=   400000
Fund left at 70 years=   50000
No of years (n)=   20
Interest rate=   6%
Present value of future value remaining = future value/(1+i)^n  
50000/(1+6%)^20=   15,590.24
So Present Value of Fund excluding Present Value of Fund left at end = 400000-15590.24=   384,409.76
So Fund amount for calcultion of Annuity (p)=   384,409.76
Annuity to be received = P* i *((1+i)^n)/((1+i)^n-1)  
384409.76 *6%*((1+6%)^20)/(((1+6%)^20)-1)  
$33,514.59  
So he will receive $33514.59 and that can be maximum spent by him per year.  
amount is not between 36000 and 37000  
Answer is false