Question

ci for two years and three years are 156 and 254 respectively. find the rate of ci

Answer 1

CI = P((1+R/100)ⁿ -1)
P((1+R/100)³-1) = 254   →(1)
P((1+r/100)²-1)= 156     →(2)
Dividing (1)/(2) and substituting (R/100) as "a" we get,
(a³-1)/(a²-1) = 254/156
Using (a³-1³) and (a²-1²)
⇒(a-1)(a²+1+a)/(a+1)(a-1) = 254/156 = 127/78
⇒(a²+1+a)/(a+1) = 127/78
78(a²+1+a) = 127(a+1)
78a²+78+78a = 127a+127
78a²-49a-49 = 0
Applying the below equation , solve for quadratic eqn... we get,
q = 7/6
we know q = (1+R/100) = 7/6
100+R = 700/6
600+6R = 700
6R = 100
R= 16.66 i.e 16²/³ % (rate of interest)






Hope it helps... :)