Read the Chapter 4 E-Book

156 PART 2 Important Financial Concepts
2. For quarterly compounding:
FV2$1001 42
$100(1 0.02) 8 0.08
$117.16
4
These results agree with the values for FV2 in Tables 4.5 and 4.6.
If the interest were compounded monthly, weekly, or daily, m would equal 12,
52, or 365, respectively.
Using Computational Tools
for Compounding More Frequently Than Annually
We can use the future value interest factors for one dollar, given in Table A–1,
when interest is compounded m times each year. Instead of indexing the table for
i percent and n years, as we do when interest is compounded annually, we index
it for (im) percent and (mn) periods. However, the table is less useful,
because it includes only selected rates for a limited number of periods. Instead, a
financial calculator or a computer and spreadsheet is typically required.
EXAMPLE Fred Moreno wished to find the future value of $100 invested at 8% interest
compounded both semiannually and quarterly for 2 years. The number of compounding
periods, m, the interest rate, and the number of periods used in each
case, along with the future value interest factor, are as follows:
Input Function
100 PV
4
4
Solution
116.99
N
I
CPT
FV
Input Function
100 PV
8
2
Solution
117.17
N
I
CPT
FV
Compounding Interest rate Periods Future value interest factor
period m (i ÷ m) (mn) from Table A–1
Semiannual 2 8% 24% 2 24 1.170
Quarterly 4 8% 42% 4 28 1.172
Table Use Multiplying each of the future value interest factors by the initial
$100 deposit results in a value of $117.00 (1.170$100) for semiannual compounding
and a value of $117.20 (1.172$100) for quarterly compounding.
Calculator Use If the calculator were used for the semiannual compounding
calculation, the number of periods would be 4 and the interest rate would be
4%. The future value of $116.99 will appear on the calculator display as
shown in the first display at the left.
For the quarterly compounding case, the number of periods would be 8 and
the interest rate would be 2%. The future value of $117.17 will appear on the calculator
display as shown in the second display at the left.
Spreadsheet Use The future value of the single amount with semiannual and
quarterly compounding also can be calculated as shown on the following Excel
spreadsheet.