58 
ON THE VALUE OF ANNUITIES. 
AMOUNT OF ANNUITIES AT SIMPLE INTEREST. 
Let s = the amount, a = the annuity, n = the number of years, i 
annual interest of £l. 
I n {n - 1) 
s + i 
‘1 
2 8 
2 n -f n (n — 1) i J 
V 8 *'j+ (2-i)*-(2-i); 
2 z 
2l 71 
n (ZZ—1) 
AMOUNT OF SUMS AT COMPOUND INTEREST. 
80. Let s — the amount, p ~ the principal, n ~ number of years, 
z = annual interest of £l. 
When the interest is payable yearly. 
s — p (1 + i) n log s = n log (1 + z) + log p. 
p = s (1 + 0" " 
log s — log p 
log p — — n log (1 + z) -f log s, 
lo,£ 
. /» _ log S — log p 
V p n 
81. When interest is convertible m times a year. 
log s = mn, log (1 + — J + log j), 
log P = — mn log (1 + — j + log s;