Question

Q7.What will be the amount and interest on the sum of ₹ 2,000 at 5 % compound interest in 3

years?​

Answer 1

${\large{\boxed{\underline{\mathrm{\bf{\orange{Given:-}}}}}}}$

• Principal = ₹2,000
• Rate of Interest = 5%
• Time = 3 years

${\large{\boxed{\underline{\mathrm{\bf{\purple{To \ Find:-}}}}}}}$

• Amount and Interest

${\large{\boxed{\underline{\mathrm{\bf{\pink{Formula \ Used:-}}}}}}}$

❶ To find Compound Interest we know that,

$\bigstar \ {\large{\boxed{\underline{\mathsf{\tt{\green{C.I. = P \bigg [ \bigg ( 1+\dfrac{R}{100} \bigg ) ^n - 1 \bigg ]}}}}}}} \ \bigstar$

where,

• C.I. = Compound Interest
• P = Principal i.e. ₹2,000
• R = Rate of Interest i.e. 5%
• n = Time i.e. 3 years

❷ To find amount we know that,

$\bigstar \ {\large{\boxed{\underline{\mathsf{\tt{\red{Amount = Principal + Interest}}}}}}} \ \bigstar$

${\large{\boxed{\underline{\mathrm{\bf{\blue{Solution:-}}}}}}}$

❶ First we have to find the compound interest,

Given :

• Principal = ₹2,000
• Rate of Interest = 5%
• Time = 3 years

According to the question by using the formula we get,

$\longmapsto {\mathsf{C.I.= 2,000 \bigg [ \bigg ( 1+\dfrac{5}{100} \bigg ) ^3 - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I.= 2,000 \bigg [ \bigg ( \dfrac{21}{20} \bigg ) ^3 - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I.= 2,000 \bigg [ \bigg ( \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} \bigg ) - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I.= 2,000 \bigg [ \dfrac{9,261}{8000} - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I. = 2,000 \times \dfrac{1,261}{8,000}}}$

$\longmapsto {\mathsf{C.I.= \dfrac{2,522}{8}}}$

$\Longrightarrow {\mathsf{Compound \ Interest = 315.25}}$

$\bigstar \ {\boxed{\underline{\mathsf{\pink{Hence, the \ Compound \ Interest \ is \ Rs. \ 315.25}}}}} \ \bigstar$

❷ Now we have to find the amount,

Given :

• Principal = ₹2,000
• Interest = ₹315.25

According to the question by using the formula we get,

$\longmapsto {\mathsf{Amount = Rs. \ (2,000 + 315.25)}}$

$\Longrightarrow {\mathsf{Amount = Rs. \ 2,315.25}}$

$\bigstar \ {\boxed{\underline{\mathsf{\blue{Hence, the \ Amount \ is \ Rs. \ 2,315.25}}}}} \ \bigstar$