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Future Value of an Annuity - DOC

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					                     Future Value of an Annuity


The Problem – I want to save an equal amount each month for the
next 40 years for my retirement. I plan on investing these
payments in stock. My goal is to have $2,000,000 saved by the
end of this time period. How much should I save each month?

An annuity is a series of equal payments made at regular intervals.
An increasing annuity is a series of equal deposits to grow an
account, such as payments into a 401(k) plan. A decreasing
annuity is a series of equal withdrawals which decreases the
balance.

In an increasing annuity, there are two increases to the
account….the interest that is credited to the current balance and the
additional payments made.

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)6  1000

.06S = 1000 1.06 6  1

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

Generalized, we can state Future Value of an Annuity =
  (1  n ) nt  1
        r
                                                       r
                                                             
D                 or inversely, Payment  FV        n
                                                             
                                              (1  n )  1
          r                                           r nt
          n




Practice: You deposit $100 each month into an increasing
annuity that pays an annual interest of 7.5%, compounded
monthly. What is the balance after 40 years?

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?

TI-83 plus – [Apps][Finance][TVM solver](fill in all information)
           [Apps][Finance][TVM_PMT]

Practice – You would like to save $500,000 for your two children’s
college education beginning in 15 years. If you save at a rate of
8%, how much should you save per month?

				
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