Question

what sum of money put at 4%p.a. compound interest for 18years will amount to rs 10000?[given,log 2= 0.3010300,log3=0.4771213 & log 7= 0.8450980]

Answer 1

let sum =p
use formula ,
A=p(1+r/100)^n

given
A=10000 Rs
p=?
r=4%
n=18 years
now,
10000=p(1+4/100)^18

10000=p(1+0.04)^18

10^4=p(1.04)^18

take both side log
log(10)^4=log{p(1.04)^18}

4=logp+log(1.04)^18

4=logp +18log(1.04)

4-18log(1.04)=logp

4-18{log(104/100)}=logp

4-18{log(104)-log(100)}=logp

4-18{log(2^3 x 13)-2}=logp

4-18{3log2+log13-2}=logp

4-18{3 x 0.301+1.11-2}=logp

4-18{0.903+1.11-2}=logp

4-18(0.013)=logp

3.766=logp

use log(a base b)=N
a=b^N

p=10^(3.766) Rs