# 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

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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