= PV(1 + i)N
1.2 is commonly referred to as the compound
amount formula. Note that it assumes the interest rate
is constant over time.
(1 + i)N the future value interest factor, FVIF, which
in the 5 year example with i = 5% equals
FVIF = (1 + i)N = 1.2763.
the FVIF, the future value can therefore be written as
= PV*FVIFi,N = $127.63.
Bill will receive $127.63 if he waits five years to withdraw the
funds from the savings account.
our definition of future value and formulation for FVN,
what would cause FVN to rise? Let's determine the effects
of each of the other variables (i, N, and PV) on the future value
formulation by examining the impact of changes in each on FVN
in Formula 1.2:
If i increases,
If N increases, FVN increases
If PV increases, FVN increases
there is a direct relationship between each of the variables and
Future Values in Excel
We can use Excel to
create a table of future values for our savings account example.
This table allows us to perform comparative statics on the
simple future value model by changing parameter and variable
values and examining the results. In addition, Excel has built-in formulas
to aid in performing the above calculation. Click
here to use the future value table and for a demonstration of the FV function in
Calculate (by hand) the future value of $1000 in four years time
given an annual interest rate of 4.25%. Confirm using the
Excel table and FV function. Answer.
Let us take a different look at the previous problem. Suppose
that Bill has the option of receiving $127.63 five years from
today or a particular sum of money, $100 today. Which would he
pick? To make the comparison we must rewrite them in terms of
their present values. We use the present value formulation to
determine the current or present value of $127.63 five years from
now. The present value is easily found by solving for PV in formula
= PV(1 + i)N
1.3 is commonly referred to as the present
value formula. Note that it also assumes the interest
rate is constant over time.
1/(1 + i)N serves to discount future values to account
for the opportunity cost of time and is called the present value
interest factor, PVIFi,N, which is simply the reciprocal
of the FVIF.
= 1/(1 + i)N
example, the PVIF.05,5 = 0.783526 which implies that
value of the $127.63 received in five years is equal to $127.63(0.783526)
= $100.00. This is exactly what we would expect.
Thus, Bill is indifferent between receiving $127.63 five years
from today and receiving $100.00 today. This is true as long as
his opportunity cost of waiting for the funds is 5% per year.
our definition of present value and formulation for PV, what would
cause PV to rise? Let's determine the effects of each of the other
variables (i, N, and FVN) on the present value formulation
by examining the impact of changes in each on PV in Formula 1.3:
If i decreases,
If N decreases, PV increases
If FVN increases, PV increases
there is an indirect relationship between i and PV, and N and
PV, and a direct relationship between FVN and PV.
value concept can be used to determine how much you would need
to deposit today in order to have a certain dollar amount saved
in the future. For example, assume you know you would like to
have a savings balance of $5,000 in three years. If your savings
account earns 3.5% per year (compounded annually), you want to
know how much would you have to save today. Using formula 1.3:
for PV = FVN[1/(1 + i)N] = 5000[1/(1 + .035)3]
if you saved $4,509.71 today in an account earning 3.5% per year,
you would have $5,000 available in three years.
Present Values in Excel
As with future values, we can use Excel to
create a table of present values for our savings account example
and perform comparative statics. Similarly, Excel has built-in formulas
to aid in performing the above calculation.
Click here to use the
present value table and for a demonstration of the PV function in
Calculate (by hand) the present value of $6000 received in four
years time given a discount rate of 4.25%. Confirm using the
Excel table and PV function. Answer.
the assignments below to confirm your understanding of the concepts
in this session and the use of Excel in computing future and present
1.1: Calculate (by hand) the future value of $5000 in six years time
given an annual interest rate of 5%. Confirm using the Excel
table and FV function.
1.2: Calculate (by hand) the present value of $8000 received in six
years time given a discount rate of 5.5%. Confirm using the
Excel table (extend the table by one year) and PV function.
1.3: Which would you rather have, $3,500 two years from today
or $4,100 six years from today? (Assume your opportunity cost
of waiting for money is 4% per year.)
1.4: Assume you would like to have $15,000 saved in 8 years.
If you can earn 5% per year on your savings, how much do you need
to deposit today to have $15,000 eight years from today?
1.5: Assume you save $12,000 today and you want it to grow
to a savings balance in the future of $18,000. How long will it
take if your account earns 4.6% interest per year (i.e. what is