Future Value of an Annuity - DOC - DOC

							                             Future Value of an Annuity


Warm-up – Brian starts saving for retirement when he is 25 years
old. He plans to retire when he is 67 and thinks he will need
$60,000 per year to live on during retirement. Trouble is, he
knows that inflation is 2.5% per year on average. Based on this
information, what will a year of his retirement cost when he is 67
(in future dollars)

Review of yesterday - An annuity is a series of equal payments
made at regular intervals, such as payments into a 401(k) plan.
The future value of an annuity sums up all the payments and the
interest that each payment generates.

Example: How much will the future value of an annuity be in
which there are annual payments of $1000 at the end of each year,
an interest rate of 6% and the annuity is for 6-years?

                                         End of year
     1                 2                 3         4                          5                 6
   1000              1000              1000      1000                       1000              1000
                                                                                              1060
                                                                                              1124
                                                                                              1191
                                                                                              1262
                                                                                              1338
                                                                         TOTAL                6975


S  1000(1.06)5  1000(1.06) 4  1000(1.06)3  1000(1.06) 2  1000(1.06)1  1000

1.06 S  1000 (1.06 ) 6  1000 (1.06 ) 5  1000 (1.06 ) 4  1000 (1.06 ) 3  1000 (1.06 ) 2  1000 (1.06 )


Subtract equation 1 from equation 2

1.06S – S = 1000(1.06)  1000
                                      6
.06S = 1000 1.06  1
                  6

           (1  0.06) 6  1
Sum = 1000
                 .06

                      (1  r ) t  1
Generalized, F = pmt                 and when you make more
                           r        
                                        (1  n ) nt  1
                                              r
than one payment per year, F = pmt                     
                                                r
                                       
                                               n       
                                                        

Example: Nancy and Jim want to save for their daughter’s
education so they make monthly deposits of $500 for 18 years in
mutual fund that consists of aggressive growth stocks. They
forecast this account will generate a return of 12%. What will the
balance be in this account at the end of the 18 years?


            (1  n ) nt  1
                  r                                    r    
If F = pmt                  , then pmt  F                
                                                       n

                                                (1  n )  1
                                                      r nt
                    r
           
                   n       
                                                           

Practice: You would like to save $2,000,000 for your retirement
in 40 years. If you invest at a rate of 10% per year, how much
should you save per month?

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Practice –Back to the beginning problem…If Brian needs to save
$3,385,194 for retirement, how much should he save per month if
he can achieve a 10% rate of return on his investments?