CP

(National Geographic (Little) Kids) #1
Again, the time line is shown at the top of the diagram, and the values as calculated
with a regular calculator are shown under Year 3. The future value of each cash flow is
found, and those FVs are summed to find the FV of the annuity due. The payments
occur earlier, so more interest is earned. Therefore, the future value of the annuity
due is larger—$331.01 versus $315.25 for the ordinary annuity.

Equation:

(2-4a)

.
The only difference between Equation 2-4a for annuities due and Equation 2-4 for
ordinary annuities is that every term in Equation 2-4a is compounded for one extra
period, reflecting the fact that each payment for an annuity due occurs one period ear-
lier than for a corresponding ordinary annuity.


  1. NUMERICAL SOLUTION:


The lower section of the time line shows the numerical solution using the first line of
Equation 2-4a. The future value of each cash flow is found, and those FVs are
summed to find the FV of the annuity, $331.01. Because this process is quite tedious
for long annuities, you probably would use the third line of Equation 2-4a:

(2-4a)


  1. FINANCIAL CALCULATOR SOLUTION


Most financial calculators have a switch, or key, marked “DUE” or “BEG” that per-
mits you to switch from end-of-period payments (ordinary annuity) to beginning-of-
period payments (annuity due). When the beginning mode is activated, the display
will normally show the word “BEGIN.” Thus, to deal with annuities due, switch your
calculator to “BEGIN” and proceed as before:

BEGIN
Inputs: 3 5 0  100

Output: 331.01

Enter N 3, I 5, PV 0, PMT 100, and then press FV to get the answer,
$331.01. Since most problems specify end-of-period cash flows, you should always switch your
calculator back to “END” mode after you work an annuity due problem.

$100a

(10.05)^3  1
0.05

b(10.05)$100(3.1525)(1.05)$331.01.

FVAn(Due)PMTa

(1i)n 1
i

b(1i)

PMT(FVIFAi,n)(1i)

PMTa

(1i)n 1
i

b(1i)

PMT a

n

t 1

(1i)n^1 t

FVAn(Due)PMT(1i)nPMT(1i)n^1 PMT(1i)n^2 PMT(1i)

Future Value of an Annuity 73

Time Value of Money 71
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