A man borrowed ₹ 20,000 for 2 years at 8% per year compound interest. Calculate:

(i) the interest for the first year.

(ii) the interest for the second year.

(iii) the final amount at the end of the second year.

(iv) the compound interest for two years.

(i) For 1st year:

P = ₹ 20,000

R = 8%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{20,000 \times 8 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{1,60,000}{100}\\[1em] = ₹ 1,600$

Hence, interest for first year = ₹ 1,600.

(ii)

$\text{Amount = P + Interest}\\[1em] = ₹ 20,000 + 1,600\\[1em] = ₹ 21,600$

For 2nd year:

P = ₹ 21,600

R = 8%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{21,600 \times 8 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{1,72,800}{100}\\[1em] = ₹ 1,728$

Hence, interest for the second year = ₹ 1,728.

(iii)

$\text{Final amount = P + Interest}\\[1em] = ₹ 21,600 + 1,728\\[1em] = ₹ 23,328$

So, final amount at the end of the second year = ₹ 23,328.

(iv)

$\text{Compound Interest = Final amount - Original Principal}\\[1em] = ₹ 23,328 - ₹ 20,000\\[1em] = ₹ 3,328$

Hence, compound interest for 2 years = ₹ 3,328.