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© 2014 Pacific Crest
365
M
ethodology
C
alculating
F
uture
V
alue
Scenario:
Find the future value of $1000 invested at 5% interest, compounded quarterly for
8 years.
Step
Explanation
1.
Identify variables
and determine if
interest is simple
or compounded
The principal
P
or present value
PV
is the amount invested. The bank or
other institution will tell you the interest rate
r
. You decide the time
t
in years
that you want to leave the money invested and untouched. If the interest is
compounded,
n
is the number of compounding periods per year.
WATCH
IT WORK!
Compound Interest:
P
= $1000
r
= 5% = .05
t
= 8
n
= 4
2.
Calculate the
amount in the
account after
the interest has
accrued.
The formula for the future value of an
account earning simple interest is:
FV P Prt
= +
The formula for the future value of an
account earning compound interest is:
1
n t
r
FV P
n
= +
Note that the rate
r
, usually given as a percent, is entered in either formula
as a decimal. Either formula can be solved for
P
, giving us a way to know the
principal or present value that needs to be invested now in order to have a
specific future value
FV
.
4 8
.05
1000 1
$1488.13
4
FV
=
+
=
3.
Validate
Use the Excel Future Value (FV) function to validate:
=FV(r,n,pmt,p)
where n is the number of compounding periods,
r
is the rate per period,
pmt
is the additional payment into the account each period, and
p
is the beginning
principal. Note that Excel uses negative values for money that you pay out
(put into the account) and positive values for amounts that you receive.
.05 ( , 32, 0, 1000)
4
FV
=
−
in Excel to get the same result
(The 0 is for additional equal payments into this account each period; none in this case.)
YOUR
TURN!
Scenario:
Find the future value of $500 invested at 8% compounded daily for 18 years.
8.2 Time Value of Money