If a certain sum at compound interest becomes ₹800 in 2 years and ₹840 in 3 years. Find the rate of interest per annum and the sum.

Option 1 : 5%, Rs. 725.63

Let, amounts be A1, A2

Amount for 2year (A1) =800

Amount for 3year (A2) =840

**Given that,**

\(840 =P(1 + \frac{R}{100})^3\) --------2

\(800 = P ( 1 + \frac{R}{100})^2\) ------------1

On dividing equation 2 by 1

\({\frac{840}{800}} \) = \(\frac{(1 +\frac{R}{100})^3}{(1 +\frac {R}{100})^2}\) ⇒ \(\frac{21}{20} =1 + \frac{R}{100} \)

∴ R = 5%

Sum = x

Amount = sum(1 + \(\frac{R}{100}\))^{2}

x\((1 + \frac{5}{100})^2\) = 800

⇒ \(\frac{105}{100} \times \frac{105}{105} \times x\) = 800

⇒ \(\frac{21}{20} \times \frac{21}{20} \times x =100 ⇒ x =\frac{800 \times 20 \times20}{ 21 \times 21}\)

\( ⇒ x =\frac{800 \times 20 \times20}{ 21 \times 21}\)

⇒ Rs. 725.63

**∴ Rate of interest = 5%, Sum = 725.63**