Lesson 39
Appendix
I Section 5.6 (part 1)
Any of you who are familiar with financial plans or retirement investments know about
annuities.
An annuity
is a plan involving payments made at regular intervals.
An
ordinary
annuity
is one in which the payments are made at the end of each time interval.
In this
lesson, we will be discussing ordinary annuities.
The
future value
of an annuity is the
sum of all the payments and the interest those
payments earn.
Suppose a person makes a payment of $500 every 3 months for 20
years.
The amount of money in that account at the end of the 20 years is the future value
of the annuity.
Formula for the Future Value of an Annuity:
The future value
S
of an ordinary
annuity with deposits or payments of
R
made regularly
k
times per year for
t
years, with
interest compounded
k
times per year at an annual rate
r
, is given by…
(1
)
1
, where
kt
i
r
S
R
i
i
k
+

=
=
Note:
The frequency of compounding per year always equals the types of payments.
For
example, if a person makes monthly payments, then the interest is compounded monthly.
If a person makes payments every 6 monthly, then the interest is compounded
semiannually.
Ex 1:
Assume that $1200 is deposited at the end of each year into an account in which
interest is compounded annually at a rate of 5%.
Find the accumulated amount
(future value) after 6 years.
Ex 2:
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 Spring '09
 Annuity, Future Value, Roger, Annual rate

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