12 
ON THE VALUE OF ANNUITIES. 
extensive of which are Hutton’s, Callet’s,Taylor’s, and Babbage’s; the 
latter of which will be found the best for this subject, as it contains the 
logarithms of numbers only, and is the most correct. 
Example. What sum will £349 7 6 amount to in 29 years at 
£3 6 8 per cent compound interest ? 
log 31 = 1.49136169 
co. log 30 = 2.52287875* 
log (1 + 0 = 0.01424044 
5 
29 
12816396 
2848088 
n log (1 + 0 = 0.41297276 
log 349,375 = 2.5432918 
log p + n log (1 + i) — 2.9562646 904,200 = £904 4 0 
20. In Table 3 are given the amounts of £\ for any number of 
years not exceeding 100 at the rates of 2. 2^. 3. 3^. 4. 4^. 5. 6. 7. 8. 9. 
and 10 per cent from Smart’s Collection of Tables, published by him 
in 1726; when the amount is required for a greater number of years 
than 100 multiply the amount opposite 100 by the amount opposite to 
the number of years equal to the excess above 100; if the amount of 
£l in 130 years be required at 3 percent, (1.03) 100 X (1.03) 30 = 
(1.03) 130 . Opposite 100 in the column headed 3 per cent we find 
(1.03) 100 = 19.21863198, and opposite 30 in the same column 
(l.O3) 30 = 2,42726247, therefore(1.03) 130 =19.21863198 X 2.42726247 
r= 46.64866412, the amount of ¿£l in 130 years. As an example of 
the use of the tables— 
What is the amount of £325 in 4 years at 5 per cent compound 
interest ? 
In 5 per cent column opposite 4 years we find 
(1.05) 4 = 1.215506 
523 = p inverted 
3.646518 
243101 
60775 
395,0394 = ¿£395 0 93 
* The logarithm the reciprocal of any quantity is equal to the logarithm of that 
quantity taken from the logarithm of unity, which is 0. In the present instance the 
logarithm of — being — 1.47712125, in order to have the decimal positive, we 
and 
in Oi 
have—1.47712125 = — 2 + (2 — 1.47712125) = 2.52287875.