ELEMENTS WHICH REDUCE VALUE
which may be reduced to
a : TW
Sm = al + )mtl al (1 + 7)m +)
~<a +m tna — 1). (9)
For the interest rate of 6 per cent: 7 = 0.06 and
p= ET irae — Fla otr=n +na—1). (10)
Form =n and i = 0.06
S, = er (1.067 — 1.06) — = (0.06 + na) (11)
= en whl — al —
3. ar (1.06 1.06) ol Tb (12)
If now the total amount in the replacement fund be compared
 with the total investment which, on the assumption made,
will be 7 dollars for each dollar of annual investment, the relation
 between the replacement and the investment expressed in
percentage and called R will be found to be:
= 1904 J ym+l __ yym—n+1
RR. = [(1 +14) (1 +19) ]
== 2a +d" tna —1] (13)
and for the interest rate of 6 per cent or i = 0.00,
R, = 2%. (1.06™*1 — 1.06m—n+1)
0.00367
- Joo m—n+1 wo
= (1.06 +na —1) (14)
and for m = n and 7 = 0.06,
100 @ 100¢ 100
= —— (1,06"*] — 1.06) — == 22
Rn 0.0036 =i 250) 0.06 n (135)
R,= 27,778 (1.06"" — 1.06) — 1667 a — i (16)

93
or
or