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 61st birthday and her last withdrawal on her 90th 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 60th 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 60th birthday

PV

=

$864,601.67

 

 

Step 2: Solve for payment needed to reach the goal

 

 

 

 

Goal for the 60th birthday

FV

=

$864,601.67

Number of deposits

N

=

35

Return

i

=

4%

 

 

 

 

Annual deposit

PMT

=

$11,738.98

 

 

 

 

 

 


 

Graph of the problemís solution