24 
ON THE VALUE OF ANNUITIES. 
By logarithms, 
log 1.05~* = 1.9788101 
10 
log 1.05-“ - 1.7881070 
log s “ 2.5440680 
2.3321750 = 214.870 = £214 17 5 
In the expression (1 + ¿)~" if i be taken = .02 and 1, 2,3, 
&c. respectively, the several values which it represents will be expressed 
by the geometrical series 1.02~ *, 1.02~ 2 , 1.02“ 3 , &c., which numbers 
respectively denote the reciprocals of the amounts of £l at 2 per cent, 
in 1, 2, 3, &c. years, the decimal values of which being found, furnish 
a table of the present values of £l at 2 per cent; when i is equal to 
.025, .03, .35, &c., and the decimal values are found, the series will 
give the present values of £l at 2-?, 3, 3j, &c. per cent. Tables of the 
present values of £l due at the expiration of any number of years not 
exceeding 100, were calculated by Mr. Smart at the rates of 2, 2^, 3, 
3^, 4, 4i, 5, 6, 7, 8, 9, and 10 per cent, to 8 figures of decimals, and 
published in his valuable collection of Tables; they have been copied 
from thence, and given in Table 4 of this work, with the whole of the 
decimals, which will be found useful where great accuracy is required. 
36. To find (s) the sum due, 
(Art. 35.) 
(1 + 0“ 
Multiplying each side by (1 + i) n (Arith. and Alg., 110.) 
V (1 + i T- 
By logarithms, log s — logp + w.log (1 + i) 
Rule. Multiply the present value by the amount of £l in the given 
time. 
Example. What sum will the present payment of £214.87 entitle 
a person to at the expiration of 10years, compound interest 5 per cent? 
n — 10 
1.628894 
78.412 “ p inverted 
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