A sum of ₹ 8,000 is invested for 2 years at 10% per annum compound interest. Calculate:

(i) interest for the first year.

(ii) principal for the second year.

(iii) interest for the second year.

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

(v) compound interest earned in 2 years.

(i) For 1st year:

P = ₹ 8,000

R = 10%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{8,000 \times 10 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{80,000}{100}\\[1em] = ₹ 800$

Hence, interest for first year = ₹ 800.

(ii)

$\text{Amount = P + Interest}\\[1em] = ₹ 8,000 + 800\\[1em] = ₹ 8,800$

So, principal for the second year = ₹ 8,800.

(iii) For 2nd year:

P = ₹ 8,800

R = 10%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{8,800 \times 10 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{88,000}{100}\\[1em] = ₹ 880$

Hence, interest for the second year = ₹ 880.

(iv)

$\text{Final amount = P + Interest}\\[1em] = ₹ 8,800 + 880\\[1em] = ₹ 9,680$

So, final amount at the end of the second year = ₹ 9,680

(v)

$\text{Compound Interest = Final amount - Original Principal}\\[1em] = ₹ 9,680 - ₹ 8,000\\[1em] = ₹ 1,680$

Hence, compound interest earned in 2 years = ₹ 1,680.