Regular Deposits And Finding Time An n u i t y A series of payments or investments made at regular intervals A simple annuity is an annuity in which the payments coincide with the compounding period An ID: 760178
Download Presentation The PPT/PDF document "8.4 Annuities: Future Value" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
8.4 Annuities: Future Value
Regular Deposits And Finding Time
Slide2Annuity
A series of payments or investments made at regular intervals.
A
simple annuity
is an annuity in which the payments coincide with the compounding period. An
ordinary annuity
is an annuity in which the payments are made at the end of each interval.
Slide3From previous lessons, you have learned how to find...
Future Value of Compounding
InterestFuture value, A, of the amount invested (in dollars $) at the beginning, $P, at the end of n compounding periods.
P = Amount Invested
r = Interest Rate Per Period
n = Number Of Compounding Periods
Slide4Future Value of an Annuity (Formula #
1)Future value of ALL investments until the LAST compounding period.
a = Amount Invested Each Period r = Interest Rate Per Period n = Number Of Compounding Periods
The formula for the
Sum of a Geometric Series
can be used to determine the future value of an annuity.
Slide5Future Value of an Annuity (Formula #2)Future value of annuity in which $R is invested at the end of each n compounding periods earning i% of compound per interval is:
Slide6Now that we know how to find FV, we can now find the values of:R The regular payment of an annuity required to reach future valuen The number of compounding periods to reach future valuet The term (number of years to pay off) of an annuity.
Slide7Example 1
Sam wants to make monthly deposits into an account that guarantees
9.6 %/a
compounded monthly
. He would like to have
$500 000
in the account at the end of
30 years
. How much should he deposit each month?
First, we must calculate
i
and
n
according to the compounding period :
i =
9.6%
= 0.096 /
12
= 0.008
n =
30 yrs
= 30 x
12
= 360
FV =
$500 000
We are now solving for
r :
r =
$ ?
Slide8Now we are able to solve for
R
, or the amount Sam should be depositing each month:
Sam would have to deposit
$240. 80
into the account each month in order to have
$500 000
at the end of
30 years
.
Slide9Example 2
Nahid
borrows
$95 000
to buy a cottage. She agrees to repay the loan by making equal monthly payments of
$750
until the balance is paid off. If
Nahid
is being charged
5.4%/a
compounded monthly
, how long will it take her to pay off the loan?
First, we must calculate
i
according to the compounding period :
i =
5.4%
= 0.054 /
12
= 0.0045
PV =
$95 000
R =
$750
We are now solving for
n :
n =
? yrs
Slide10Take a look at your handout for solution.