To find the rate of compound interest per annum at which a sum of Rs. 1200 becomes Rs. 1348.32 in 2 years, we use the compound interest formula for the amount:
A=P(1+R100)nA=P\left(1+\frac{R}{100}\right)^nA=P(1+100R)n
Where:
- A=1348.32A=1348.32A=1348.32 (final amount)
- P=1200P=1200P=1200 (principal)
- n=2n=2n=2 years
- RRR = rate of interest per annum (unknown)
Substituting the values:
1348.32=1200(1+R100)21348.32=1200\left(1+\frac{R}{100}\right)^21348.32=1200(1+100R)2
Divide both sides by 1200:
1348.321200=(1+R100)2\frac{1348.32}{1200}=\left(1+\frac{R}{100}\right)^212001348.32=(1+100R)2
1.1236=(1+R100)21.1236=\left(1+\frac{R}{100}\right)^21.1236=(1+100R)2
Taking the square root of both sides:
1.1236=1+R100\sqrt{1.1236}=1+\frac{R}{100}1.1236=1+100R
1.06=1+R1001.06=1+\frac{R}{100}1.06=1+100R
Solving for RRR:
R100=1.06−1=0.06\frac{R}{100}=1.06-1=0.06100R=1.06−1=0.06
R=6%R=6%R=6%
Therefore, the rate of compound interest per annum is 6%. This matches the detailed solutions found in multiple sources
