Find the amount and the compound interest on ₹ 64,000 for $1\dfrac{1}{2}$ year at 15% per annum, compounded half-yearly.

Given,

Rate = 15%

Half yearly rate (R) = $\dfrac{\text{Rate}}{2} = \dfrac{15\%}{2}$ = 7.5%

Time = $1\dfrac{1}{2}$ year = $\dfrac{3}{2} \times 2$ = 3 half-year.

For first half year :

P = ₹ 64,000

T = 1 half year

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

$= \dfrac{64,000 \times 7.5 \times 1}{100}$ = ₹ 4,800

Amount = P + I = ₹ 64,000 + ₹ 4,800 = ₹ 68,800

For second half year :

P = ₹ 68,800

Half yearly rate (R) = 7.5%

T = 1 half year

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

$= \dfrac{68800 \times 7.5 \times 1}{100}$ = ₹ 5,160.

Amount = P + I = ₹ 68,800 + ₹ 5,160 = ₹ 73,960.

For third half year :

P = ₹ 73,960

Half yearly rate (R) = 7.5%

T = 1 year

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

$= \dfrac{73960 \times 7.5 \times 1}{100}$ = ₹ 5,547.

Amount = P + I = ₹ 73,960 + ₹ 5,547 = ₹ 79,507.

Compound interest = Final amount - Initial principal

= ₹ 79,507 - ₹ 64,000 = ₹ 15,507.

Hence, final amount = ₹ 79,507 and compound interest = ₹ 15,507.