Question

find the compound interest on rupees 60000 at the rate of 10 percent per annum 3 half years when interest is compounded half yearly
​

Answer 1

Given :

• Principal = Rs.60000
• Rate = 10 %
• Time = 1.5 year or 3 half years

$\rule{200pt}{3pt}$

To Find :

• Compound Interest = ?

$\rule{200pt}{3pt}$

Solution :

☢ Formula Used :

• Compounded Half - Yearly :

$\large{\pink{\bigstar}} \: \: {\underline{\boxed{\purple{\sf{ C.I = P \bigg\lgroup 1 + \dfrac{\dfrac{R}{2}}{100} \bigg\rgroup ^{2 \times T} - P }}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

☢ Calculating the Compound Interest :

${\dashrightarrow{\qquad{\sf{ C.I = P \bigg\lgroup 1 + \dfrac{\dfrac{R}{2}}{100} \bigg\rgroup ^{ 2 \times T} - P }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 60000 \bigg\lgroup 1 + \dfrac{\cancel\dfrac{10}{2}}{100} \bigg\rgroup ^{ 2 \times 1.5} - 60000 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 60000 \bigg\lgroup 1 + \cancel\dfrac{5}{100} \bigg\rgroup ^{ 3} - 60000 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 60000 \bigg\lgroup 1 + 0.05 \bigg\rgroup ^{3} - 60000 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{C.I = 60000 \bigg\lgroup 1.05 \bigg\rgroup ^{3} - 60000 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 60000 \times 1.05 \times 1.05 \times 1.05 - 60000 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 60000 \times 1.157625 - 60000 }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ C.I = 69457.5 - 60000 }}}} \\ \\ \ {\qquad{\sf{ Compound \: Interest \: = {\color{green}{\pmb{\sf{ ₹ \: 9457.5(Approx.) }}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

☢ Therefore :

❝ Compound Interest on this amount for 3 half years at 10 % is ₹ 9457.5(Approx.) . ❞

${\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt}{\red{\rule{100pt}{5pt}{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt} }}}}}}}}}}$

Answer 2

Given:-

• Principal = ₹ 60000
• Rate = 10%
• n = 3 half year

To Find:-

• When interest is compounded half yearly.

Solution:-

When interest is compounded half yearly.

then,

• Rate = 10/2=5% conversion period.

$A = P(1 + \frac{R}{100} ) {n}^{}$

$= 60000(1 + \frac{5}{100} ) {}^{3}$

$= 60000 \times (\frac{105}{100} ) {}^{3}$

$= 60000 \times \frac{105}{100} \times \frac{105}{100} \times \frac{105}{100}$

$= 69457.5$

$compound \: interest \: = \: amount \: - \: principal$

$compound \: interest \: = 69457.5 - 60000$

$= 9457.5$

Hence,

• 9457.5 interest is compounded half yearly