• We no w consider the case where the payments are made more fre-
quently than interest con version.
• Let there be mn pa ym ents for an ann uity-imm ediate occurring at
time 1/m, 2/m, ···, 1, 1+1/m, ···, 2, ···, n,andleti be the effective
rate of interest per in terest-conversion period. Thus, there are mn
payments ov er n interest-con version periods.
• Suppose eac h payment is of the amount 1/m, so that there is a
nominal am ount of unit pa ym ent in eac h interest-conv ersion period.
• Figure 2.7 illustrates the cash flows for the case of m =4.
• We denote the present value of this annuity at time 0 by a
(m)
n
e
i
,which
can be computed as follows (we let w = v
1
m
)
a
(m)
n
e
i
=
1
m
³
v
1
m
+ v
2
m
+ ···+ v + v
1+
1
m
+ ···+ v
n
´
30