Question

Find the compound interest on 24000 compounded semi annually for 3/2 years at the rate of 10%p.a​

Answer 1

${\large{\bf{\pink{✯ \: \: {\underline{\underline{ Given}}} \: \: ✯}}}}$

• Principal = 24000
• Number of years = ${\sf{ \frac{3}{2} }}$
• Rate = 10% p.a

${\large{\bf{\pink{✯ \: \: {\underline{\underline{ To \: \: find }}} \: \: ✯}}}}$

• Compound Interest

${\Large{\bf{\red{ ꧁ \: \: {\underline{\underline{Solution}}} \: \: ꧂}}}}$

Here 3/2 is compounded semi - annually because 3×1/2 months are there , So, :-

$\: \: \: \: \: \: {\footnotesize{\bf{\implies {n = \frac{ \frac{3}{2} }{ \frac{1}{2} } }}}}\\ \: \: \: \: \: \: {\footnotesize{\bf{\implies {n = 3 ×\frac{1}{2}×2}}}} \\ {\footnotesize{\bf{\implies {n = \frac{6}{2} }}}} \\ {\footnotesize{\implies{ \underline{{{ \boxed{ \bf{ {n =3}}}}}}}}}$

And also rate is halved:-

$\\ {\footnotesize{\bf{\implies {n = \frac{10}{2} }}}} \\ \: \: {\footnotesize{\implies{ \underline{ \boxed{ \bf {n =5\%}}}}}}$

So, we have :-

• Principal = 24000 rs
• Number of year = 3
• Rate = 5%

Amount:-

$\\ {\large{\bf{\implies{Amount= P(1 + \frac{r}{100}) ^{n} }}}}$

$\\ {\large{\bf{\implies{Amount= 24000(1 + \frac{5}{100}) ^{3} }}}}$

$\\ {\large{\bf{\implies{Amount= 24000(1 + \frac{1}{20}) ^{3} }}}}$

$\\ {\large{\bf{\implies{Amount= 24000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} }}}}$

$\\ {\large{\bf{\implies{Amount= 24 \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2} }}}}$

$\\ {\large{\bf{\implies{Amount= 3 \times 21 \times 21 \times 21 }}}}$

$\\ { \underline{ \boxed{ \blue{\large{\bf{\implies{Amount= 27,783 \: \: rs}}}}}}}$

So, Compound Interest is :-

${\large{\bf{\leadsto{C.I=27783−24000}}}}$

$\\ { \underline{ \boxed{ \green{\large{\bf{\implies{CI=3783 \: \: rs}}}}}}}$

So, Compound Intrest is Rs 3783.

.

Answer 2

♧Answer♧

• Principal= 24,000

• Time= 3/2 years

• Rate= 10% p.a

Semi-annually 3×(1/2) months are there. So,

n = (3/2)÷(1/2)

By further solving

n = 3

r = 10% but for half year r = 10/2 => 5%

Amount

= P {1+(r/100)}^n

= 24000(1+0.05)3

24000(1+0.05)3=24000×1.05×1.05×1.05

• Amount = 27783

CI = Amount–Principal

CI = 27783 – 24000

24000CI =3783.