OF INTEREST AND ASKL'JTIES. 
238 
therefore, by Tkcor. l, log. m ( = log. A f log. R R j 
— log. R—7) = log. 50 + log. imF : — 1. — log. ,04 
■— 2,596597; and consequently m - 395 i. the value 
that was to be found. 
Examp. 2. What annuity, forborne seven years, will 
amount to, or raise a stock of 395/. at 4 per.cent, com 
pound interest ? 
In this case we have given R — 1,01, v — 7, and 
m — 395; whence, by Theorem 2, log. A ( =r log. m. 
— log. R» — 1 +- log. R — 1 ) — log. 395 — log. 
1,041 7 — 1 -f log. ,04 := 1,6989700; and consequently 
A — 50/. which is the annuity required. 
Examp. 3. In how long time will 50/. annuity raise 
a stock of 395/. at 4 per cent, per annum, compound 
interest ? 
Here we have R n 1,04, A = 50, m — 395; and 
therefore, by Thcor. 3, n ( rr }/ L 1 ^ 1°^-, 
V ÌógTli ' 
,0170333' “ *’ 1 number of years required. 
Examp. 4. If 120/. annuity, forborne eight years, 
amounts to, or raises a.stock of 1200/. what is the rate 
of interest? 
In this case we have g iven n — 8, A = 120, and m 
rr 1200, to tind-R; therefore, by Theorem 4, we have 
R s — 10R + 9 = 0, from which, by any of the methods 
in Sect. 13, ■ the required value of R will be found = 
!,06287 ; therefore the rate is 6,287, or 6l.bs.9d. 
per cent, per annum. 
The solution of the last case, where the rate is re 
quired, being a little troublesome, I shall here put down 
an approximation (derived from the third general 
formula, at p. 1.65) which will be found to answer 
very near the truth, provided the number of years is 
not very great.