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 com- 
pared with the total investment which, on the assumption made, 
will be 7 dollars for each dollar of annual investment, the rela- 
tion 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