The simple interest on a certain sum of money for 3 years at 5% per annum is ₹ 1200. Find the amount due and the compound interest on this sum of money at the same rate and after 2 years, interest is reckoned annually.

Let sum of money be ₹ x.

For S.I. :

P = ₹ x

Rate = 5%

Time = 3 years

S.I. = $\dfrac{P \times R \times T}{100} = \dfrac{x \times 5 \times 3}{100} = \dfrac{3x}{20}$.

Given,

S.I. = ₹ 1200

$\therefore \dfrac{3x}{20} = 1200 \\[1em] \Rightarrow x = \dfrac{1200 \times 20}{3} = ₹ 8000.$

When rate is compounded annually:

$A = P\Big(1 + \dfrac{r}{100}\Big)^n \\[1em] = x \times \Big(1 + \dfrac{5}{100}\Big)^2 \\[1em] = 8000 \times \Big(\dfrac{105}{100}\Big)^2 \\[1em] = 8000 \times \Big(\dfrac{21}{20}\Big)^2 \\[1em] = ₹ 8820.$

C.I. = A - P = ₹ 8820 - ₹ 8000 = ₹ 820.

Hence, amount due = ₹ 8820 and C.I. = ₹ 820.