[4 17 5 
02 and n— 1, 2,3, 
its will be expressed 
&c., which numbers 
of £l at 2 per cent, 
being found, furnish 
when i is equal to 
found, the series will 
cent. Tables of the 
number of years not 
the rates of 2, 2j, 3, 
ares of decimals, and 
icy have been copied 
vith the Avhole of the 
iccuracy is required. 
ndAlg., 110.) 
mt of £l in the given 
at of £214.87 entitle 
ad interest 5 per cent ? 
: ‘05 
log (1 + i) 
Rule. From the logarithm of the sum due, subtract the logarithm of 
the present value, and divide the difference by the logarithm of the 
amount of £l in one year. 
Example. A person at the end of a certain number of years, has to 
pay £350 for the renewal of a lease, but wishing to pay some time 
before the expiration of the term, he is allowed a discount of 5 per cent, 
compound interest, which reduces the payment to £214.87; how many 
years had the lease to run ? 
s = 350 p = 214.87 i - .05 
log s =: 2,5440680 
log j) = 2.3321750 
log 1.05 
.0211893)0.2118930 (10 years 
2118930 
38. To find (i) the rate of interest: 
(Art. 36.) s — p (1 4- i) n , 
from which is found by the solution of that equation in Art. 23, 
Rule. Divide the difference between the logarithms of the sum due 
and the present value by the number of years, and from the correspond 
ing number subtract one, the result is the interest of £l; this mul 
tiplied by 100, gives the rate per cent. 
Example. A debt of £350 is due from A to B, payable at the ex 
piration of 10 years, which A is allowed to discharge by the immediate 
payment of £214.87 ; what rate per cent compound interest is allowed ? 
» = 350 p “ 214.87 
log s " 2.5440680 
logp ~ 2.3321750 
n — 10