Deferred Annuity Problem
Example
and Explanation
Mora Money wants to save for her retirement. Her goal is to retire at 60 years of age and
have $50,000 per year to live on for thirty years, with the first withdrawal on
her 61^{st} birthday and her last withdrawal on her 90^{th}
birthday. Mora is 25 years old today
and wants to begin making deposits to save for her retirement beginning next
year, with the last deposit on her 60^{th} birthday. She figures she can earn 4% on her
investments. How much must Mora deposit
each year to meet her retirement objective?
Step 1: Solve for balance needed prior to retirement
Withdrawal
during retirement 
PMT 
= 
$50,000 
Number
of withdrawals 
N 
= 
30 
Discount
rate 
i 
= 
4% 




Balance
in the account on the 60^{th} birthday 
PV

= 
$864,601.67 
Step 2: Solve for payment needed to reach the goal




Goal
for the 60^{th} birthday 
FV 
= 
$864,601.67 
Number
of deposits 
N 
= 
35 
Return 
i 
= 
4% 




Annual
deposit 
PMT

= 
$11,738.98 




Graph of the problem’s solution