Question

$\mathbb \purple{QUESTION : }$
Find the compound interest on 15,625 for 18 months at the rate of 8 % p.a. . Find the compounded Semi-annually.

Answer this Question
by explanation ...

Give answers in best way ..​

Answer 1

Given :

• Principal = Rs.15625
• Time = 18 months
• Rate = 8 %

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

To Find :

• Compound Interest = ?

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

Solution :

~ Formula Used :

${\color{cyan}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ C.I = P \bigg[ 1 + \dfrac{R}{200} \bigg]^{2n} - P }}}}}$

Where :

• A = Amount = ?
• Principal = Rs.15625
• R = Rate = 8 %
• T = Time = 18 Months or 1.5 years

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

~ Calculating the Compound Interest :

$\; \; \dashrightarrow \sf \: \: \: { C.I = P \bigg[ 1 + \dfrac{R}{200} \bigg]^{2n} - P }$

$\; \; \dashrightarrow \sf \: \: \: { C.I = 15625 \bigg[ 1 + \dfrac{8}{200} \bigg]^{2 \times 1.5} - 15625 }$

$\; \; \dashrightarrow \sf \: \: \: { C.I = 15625 \bigg[ 1 + \cancel\dfrac{8}{200} \bigg]^{2 \times 1.5} - 15625 }$

$\; \; \dashrightarrow \sf \: \: \: { C.I = 15625 \bigg[ 1 + 0.04 \bigg]^{2 \times 1.5} - 15625 }$

$\; \; \dashrightarrow \sf \: \: \: { C.I = 15625 \bigg[ 1.04 \bigg]^{2 \times 1.5} - 15625 }$

$\; \; \dashrightarrow \sf \: \: \: { C.I = 15625 \bigg[ 1.04 \bigg]^{3} - 15625 }$

$\; \; \dashrightarrow \sf \: \: \: { C.I = 15625 \times 1.04 \times 1.04 \times 1.04 - 15625 }$

$\; \; \dashrightarrow \sf \: \: \: { C.I = 15625 \times 1.124864 - 15625 }$

$\; \; \dashrightarrow \sf \: \: \: { C.I = 17576 - 15625 }$

${\qquad{\textsf{ Compound Interest on this sum of Money = {\orange{\sf{₹ \; 1951 }}}}}}$

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

~ Therefore :

$\large{\pink{\underline{\color{darkblue}{\underline{\pmb{\frak{ Compound \; Interest = ₹ \; 1951 }}}}}}}$

$\\ {\underline{\rule{300pt}{9pt}}}$

Answer 2

Answer:

Given :-

• A sum of Rs 15,625 for 18 months at the rate of 8% p.a.

To Find :-

• What is the compound interest semi-annually.

Formula Used :-

$\clubsuit$ Amount Formula :

$\longrightarrow \sf\boxed{\bold{\pink{A =\: P\Bigg(1 + \dfrac{\dfrac{r}{2}}{100}\Bigg)^{2n}}}}$

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time Period

$\bigstar$ Compound Interest Formula :

$\longrightarrow \sf\boxed{\bold{\pink{Compound\: Interest =\: A - P}}}$

where,

• A = Amount
• P = Principal

Solution :-

Given :

• Principal = Rs 15625
• Time = 18 months = 18/12 years = 3/2 years
• Rate of Interest = 8% p.a

According to the question by using the formula we get,

$\implies \sf A =\: 15625\Bigg(1 + \dfrac{\dfrac{\cancel{8}}{\cancel{2}}}{100}\Bigg)^{(\cancel{2} \times \frac{3}{\cancel{2}})}$

$\implies \sf A =\: 15625\bigg(1 + \dfrac{4}{100}\bigg)^3$

$\implies \sf A =\: 15625\bigg(\dfrac{100 + 4}{100}\bigg)^3$

$\implies \sf A =\: 15625\bigg(\dfrac{104}{100}\bigg)^3$

$\implies \sf A =\: 15625\bigg(\dfrac{104}{100} \times \dfrac{104}{100} \times \dfrac{104}{100}\bigg)$

$\implies \sf A =\: 15625\bigg(\dfrac{1124864}{1000000}\bigg)$

$\implies \sf A =\: 15625 \times \dfrac{1124864}{1000000}$

$\implies \sf A =\: \dfrac{17576\cancel{000000}}{1\cancel{000000}}$

$\implies \sf\bold{\purple{A =\: Rs\: 17576}}$

Now, we have to find the compound interest :

Given :

• Amount = Rs 17576
• Principal = Rs 15625

According to the question by using the formula we get,

$\dashrightarrow \sf Compound\: Interest =\: Rs\: 17576 - Rs\: 15625$

$\dashrightarrow \sf\bold{\red{Compound\: Interest =\: Rs\: 1951}}$

$\therefore$ The compound interest is Rs 1951 .