The simple interest on a certain sum of money for 2 years at 10% per annum is ₹1600. Find the amount due and the compound interest on this sum of money at the same rate after 3 years, interest being reckoned annually.

Let the sum of money be ₹x.

Given, simple interest = ₹1600.

$\therefore 1600 = \dfrac{P \times R \times T}{100} \\[1em] \Rightarrow 1600 = \dfrac{x \times 10 \times 2}{100} \\[1em] \Rightarrow 1600 = \dfrac{20x}{100} \\[1em] \Rightarrow 160000 = 20x \\[1em] \Rightarrow x = \dfrac{160000}{20} \\[1em] \Rightarrow x = ₹8000.$

Principal for first year = ₹8000.

Interest for the first year = ₹ $\dfrac{8000 \times 10 \times 1}{100} = \dfrac{80000}{100}$ = ₹800.

Amount after one year = ₹8000 + ₹800 = ₹8800.

Principal for the second year = ₹8800.

Interest for the second year = ₹ $\dfrac{8800 \times 10 \times 1}{100} = \dfrac{88000}{100}$ = ₹880.

Amount after 2 years = ₹8800 + ₹880 = ₹9680.

Principal for the third year = ₹9680.

Interest for the third year = ₹ $\dfrac{9680 \times 10 \times 1}{100} = \dfrac{96800}{100}$ = ₹968

Amount after 3 years = ₹9680 + ₹968 = ₹10648

Compound interest = Final amount - Principal = ₹10648 - ₹8000 = ₹2648.

Hence, the amount and compound interest due = ₹10648 and ₹2648 respectively.