Find the amount and the compound interest on ₹ 10,000 for 1 year at 12% per annum, compounded half-yearly.

Given,

Rate = 12%

Half yearly rate (R) = $\dfrac{\text{Rate}}{2} = \dfrac{12}{2}$ = 6%

For first half year :

P = ₹ 10,000

T = 1 half year

I = $\dfrac{P \times R \times T}{100}$

$= \dfrac{10000 \times 6 \times 1}{100}$ = ₹ 600.

Amount = P + I = ₹ 10,000 + ₹ 600 = ₹ 10,600.

For second half year :

P = ₹ 10,600

T = 1 half year

Half yearly rate = 6%

I = $\dfrac{P \times R \times T}{100}$

$= \dfrac{10600 \times 6 \times 1}{100}$ = ₹ 636.

Amount = P + I = ₹ 10,600 + ₹ 636 = ₹ 11,236.

Compound interest = Final amount - Initial principal

= ₹ 11,236 - ₹ 10,000 = ₹ 1,236.

Hence, final amount = ₹ 11,236 and compound interest = ₹ 1,236.