Chapter 5 Time Value of Money 137is “Begin” or “Begin Mode” or “Due” or something similar. If you make a mistake
and set your calculator on Begin Mode when working with an ordinary annuity,
each payment will earn interest for one extra year. That will cause the compounded
amounts, and thus the FVA, to be too large.
The last approach in Table 5-3 shows the spreadsheet solution using Excel’s
built-in function. We can put in! xed values for N, I, and PMT or set up an Input
Section, where we assign values to those variables, and then input values into the
function as cell references. Using cell references makes it easy to change the inputs
to see the effects of changes on the output.
SEL
F^ TEST For an ordinary annuity with! ve annual payments of $100 and a 10% inter-
est rate, how many years will the! rst payment earn interest? What will this
payment’s value be at the end? Answer this same question for the! fth pay-
ment. (4 years, $146.41; 0 years, $100)
Assume that you plan to buy a condo 5 years from now, and you estimate
that you can save $2,500 per year. You plan to deposit the money in a bank
that pays 4% interest, and you will make the! rst deposit at the end of the
year. How much will you have after 5 years? How will your answer change if
the interest rate is increased to 6% or lowered to 3%? ($13,540.81;
$14,092.73; $13,272.84)5-8 FUTURE VALUE OF AN ANNUIT Y DUE
Because each payment occurs one period earlier with an annuity due, all of the
payments earn interest for one additional period. Therefore, the FV of an annuity
due will be greater than that of a similar ordinary annuity. If you went through the
step-by-step procedure, you would see that our illustrative annuity due has an FV
of $331.01 versus $315.25 for the ordinary annuity.
With the formula approach, we! rst use Equation 5-3; but since each payment
occurs one period earlier, we multiply the Equation 5-3 result by (1 # I):
FVAdue! FVAordinary(1 " I) 5-4
Thus, for the annuity due, FVAdue = $315.25(1.05) = $331.01, which is the same
result when the period-by-period approach is used. With a calculator, we input the
variables just as we did with the ordinary annuity; but now we set the calculator
to Begin Mode to get the answer, $331.01.
SEL
F^ TEST Why does an annuity due always have a higher future value than an ordinary
annuity?
If you calculated the value of an ordinary annuity, how could you! nd the
value of the corresponding annuity due?
Assume that you plan to buy a condo 5 years from now and you need to
save for a down payment. You plan to save $2,500 per year (with the! rst
deposit made immediately), and you will deposit the funds in a bank account
that pays 4% interest. How much will you have after 5 years? How much will
you have if you make the deposits at the end of each year? ($14,082.44;
$13,540.81)