6 The theory of interest
Thus, an altérnate defmition is:
The effective rate of interest i is the ratio ofthe amount of interest eamed during the period to theamount of principal invested at the beginning of the period.
The same four observations made above also apply to this altérnate defmition.
Effective rates of interest can be calculated over anymeasurement period. Let in be the effective rate of interest during the nth period from the date of investment. Thenwehave
._-n = 1,2,3,... .
= v ' — '- =Within this notational framework, the "i" in formula (1.4a) might more properly be labeled i,.
Although formula (1.4b) allows the various effecüve rates of interest /„ to vary for different n, it willbe demonstrated in Section 1.5 that for one very important accumulation function, the effecüve rate of interest is constant over successive measurement periods, i.e. for all n = 1,2,3,....
Example1.2 For the $10,000 investment given in Example U, find tht effective rate of interest for each ofthe four years.
From the table of valúes given in Example 1.1 we can apply formula (1.4&) four túneltoobtaia:
; = '
_A(4)-A(3) _ 12.153.96-11.575.20 "_ 0«
A(3) ~ 11,575.20
i «1.4 SIMPLE INTEREST
!¡í It was shown in the preceding sections that a(0) = 1 and a(\) - 1 + í. There
are an infinite number ofaccumulation functions that pass through (hese two Upoints. Two of these are most significant in practice. The first, simple interest, s will be discussed in this section; and the second, compoundinterest, will be
discussed in Section 1.5.
Consider the investment of one unit such that the amount of interest earned
during each period is constant. The accumulated valué of 1 at the end of the...