Compound and Discount Factor Tables There are different ways to translate values forward and backward in

Compound and Discount Factor Tables There are different ways to translate values forward and backward in

time. The basic way is through equations (7-1) and (7-5), using which- ever values of PV, FV, N, or i given, and solving for the present or future value required by the problem.

FOUNDATIONS

Another way is to use tables of discount factors and compound fac- tors. A table of compound factors for periods ranging from 1 to 20 and for rates of interest from 1% to 15% is provided in Exhibit 7.4. Simi- larly, a table of discount factors for the same range of periods and inter- est rates is provided in Exhibit 7.5. The compound factor to use for a problem is determined by choosing the table value corresponding to the row for the number of periods and the column for the interest rate per period given in the problem. A discount factor is determined in a like manner.

To see how to use a table of factors, let’s find the compound factors for several combinations of periods and interest rates. The compound factor for 10 periods and an interest rate of 5% per period is 1.6289. The compound factor for five periods and an interest rate of 10% per period is 1.6105. The compound factor for three periods and an interest rate of 6% per period is 1.1910.

The table of compound factors can also be used for situations where you need to determine the number of periods or the interest rate. For example, suppose that you are asked to find out how long it takes to double your money if the interest rate per period is 8%. Doubling your money would mean that the future value is twice the present value. Using the equation:

FV = PV (1 + i) N

and inserting the known values: 2.0000 = 1.0000 1 ( + 0.08 ) N or 2.0000 = ( 1 + 0.08 ) N the compound factor is 2.0000.

The compound factor for 8% per period over some unknown num- ber of periods is 2.0000. Looking at the top panel, going down the 8% interest rate column, we see that the factor closest to 2.0000 is nine periods (compound factor = 1.9990). Therefore, it takes nine periods to double your money if interest is compounded at 8% per period.

Consider another example. If you want to invest $1,000 for six peri- ods, at what interest rate must the account pay compounded interest in order for you to have $1,500 after six periods? We know

FV = PV 1 ( + i N ) $1,500 = $1,000 1 ( + i 6 ) 1.5000 = ( 1 + i 6 )

EXHIBIT 7.4 Table of Compound Factors

Number of

Compounding Rate

EXHIBIT 7.5 Table of Discount Factors

Number of

Discount Rate

Mathematics of Finance

Therefore, the compound factor is 1.5. Using Exhibit 7.4, we see going across the row corresponding to six periods that the compound factor is 1.5000 at (approximately) a 7% interest rate. Therefore, if you save $1,000 in an account that provides 7% per period compounded interest for 6 periods, you will have a balance of approximately $1,500 after six periods.

To see how to use Exhibit 7.5, let’s find the discount factors for sev- eral combinations of periods and interest rates. The discount factor for ten periods and an interest rate of 5% per period is 0.6139. The dis- count factor for five periods and an interest rate of 10% per period is 0.6209. The discount factor for three periods and an interest rate of 6% per period is 0.8396. Just as we did for the compound factors, these dis- count factors can be used to solve for N, given a value of the discount factor and an interest rate, or to solve for the interest rate, given the value for the discount factor and the number of discounting periods.

If we look at equations (7-1) and (7-5) and think about them for a moment, it becomes apparent that inverting the values in one table pro- duces the values in the other. For example, using the corresponding fac- tors for N = 10 and r = 5%, we see this inverse relation:

Compound factor = ⁄ 1 Discount factor 1.6289 = ⁄ 1 0.6139

Likewise,

Discount factor = ⁄ 1 Compound factor 0.6139 = ⁄ 1 1.6289

The compound and discount factors are inversely related to one another for any pair of N and i values.