22. Cindy is 25 years old today and is beginning to plan for her retirement. She

Question

22. Cindy is 25 years old today and is beginning to plan for her retirement. She wants to set aside an equal amount at the end of each of the next 30 years so that she can retire at age 55. She expects to live to the maximum age of 90 and wants to be able to withdraw $95,000 per year from the account on her 56th through 90th birthdays. The account is expected to earn 5% per annum for the entire period of time. Determine the size of the annual deposits that must be made by Cindy.

A. $21,980.86

B. $23,413.24

C. $95,000.00

D. 17,149.26

Explanation / Answer

Calculating worth of Cindy's account on her 55th birthday
FV = 0 i.e. she has zero balance on her 90th birthday after withdrawing 95000
PMT = equal amount she withdraws every year = 95000
N= Time to maturity = 35
I/Y= interest earned = 5%
Using financial calculator to solve for PV using above values, we get PV= 1555548

Worth of Cindy's account on her 55th birthday is 1555548
Calculation of PMT
PV = present worth of Cindy's account on her 25th birthday = 0
I/Y= Interest earned = 5%
N=Time to maturity = 30years
FV = Future value of Cindy's account on her 55th birthday = 1555548

Using financial calculator, solving for PMT, using above values,
PMT = $23413.24
Hence the correct answer is B

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