ON THE VALUE OF ANNUITIES. 
By logarithms, 
log 1.02 = 0.008600171 
50 = mn 
log (1.02) 50 = 0.43000855 
log P = 2.5120004 
log s = 2.9420090 875,001 as before. 
A person invests £5000 in the 3 per cent consols when stocks are 90: 
what will this sum amount to in 15 years, supposing the interest as it 
becomes due to be always invested at the same rate ? 
3 1 
p = 5000, i = —- = —, n = 15, m = 2, the interest in the funds 
log 61 = 1.785329835 
log 60 = 1.778151250 
log p — 3.6989700 
log s = 3.9143276 = 8209.706 =£8209 14 1^ 
25. The fluctuations in the prices of the funds prevent us from 
ascertaining with precision what will be the amount of an investment 
with the accumulated dividends in a given time, as it is not probable 
that the dividends will all be invested at the original rate ; it is there 
fore necessary, if we wish to anticipate what the amount will be, to 
assume a probable average rate of interest on which our calculation shall 
be grounded. 
26. The advantage derived from the interest of money being received 
at more intervals than one in the year, will not be of much importance 
for the term of one year ; but when money is put out in this way for a 
long time, the difference becomes more considerable. The following 
formula will show the difference in the amount of interest of £l for one 
year. 
1 + -) -(i+O ; the first part of the expression being expanded 
by the binomial theorem (Ariih. and Alg. 275), and the remaining part 
subtracted, it becomes-^- i 2 + 
m — 1 m — 2 
2 m 
2m' 3 in 
equal to nearly. 
¿ 4 +, &c., which, as the series converges very fast, is