Question

RIGHT ANS WILL MARK AS BRAINLIEST

Find the compound interest on 8000 at 15% for 1 year, if the interest is compounded semi-annually​

Answer 1

Step-by-step explanation:

i hope this answer will help you

PLEASE MAKE ME AS A BRAINLIST

Answer 2

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

• Principal = ₹8,000
• Rate of Interest = 15% per half year
• Time = 1 year

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

• Compound Interest, if it is compounded semi-annually.

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

${\pink{\bigstar}} \ {\boxed{\tt{\green{C.I. = P \ \bigg [ \bigg ( 1 + \dfrac{\frac{R}{2}}{100} \bigg )^{ n \times 2} - 1 \bigg ] }}}} \ {\pink{\bigstar}}$ ------ [semi-annually]

Where,

• C.I. = Compound Interest
• P = Principal i.e.  8,000
• R = Rate i.e. 15%
• T = Time i.e. 1 year

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

Let, the time be n,

Given :-

• Principal = ₹8,000
• Rate of Interest = 15% per half year
• Time = 1 year

According to the question by using the formula of Compound Interest, we get,

$: \ \longmapsto {\mathsf{ \ 8,000 \ \bigg [ \bigg ( 1 + \dfrac{\frac{15}{2}}{100} \bigg ) ^{1 \times 2} - 1 \bigg ] }}$

$: \ \longmapsto {\mathsf{ \ 8,000 \ \bigg [ \bigg ( 1 + \dfrac{7.5}{100} \bigg ) ^{2} - 1 \bigg ] }}$

$: \ \longmapsto {\mathsf{ \ 8,000 \ \bigg [ \bigg ( \dfrac{100 + 7.5}{100} \bigg ) ^{2} - 1 \bigg ] }}$

$: \ \longmapsto {\mathsf{ \ 8,000 \ \bigg [ \bigg ( \dfrac{107.5}{100} \times \dfrac{107.5}{100} \bigg ) - 1 \bigg ] }}$

$: \ \longmapsto {\mathsf{ \ 8,000 \ \bigg [ \dfrac{11,556.25}{10,000} - 1 \bigg ] }}$

$: \ \longmapsto {\mathsf{ \ 8,000 \ \bigg [ \dfrac{11,556.25-100}{10,000} \bigg ] }}$

$: \ \longmapsto {\mathsf{ \ 8,000 \times \dfrac{11,456.25}{10,000}}}$

$: \ \longmapsto {\mathsf{ \ 0.8 \times 11,456.25}}$

$: \ \longmapsto {\mathsf{\bf{ \ 9,165}}}$

${\orange{\bigstar}} \ {\underline{\boxed{\mathsf{\green{\therefore Compound \ Interest}{\red{ \ is \ }{\blue{\bf{9,165}}}}}}}} \ {\orange{\bigstar}}$

${\huge{\green{\checkmark}}} \ {\large{\boxed{\underline{\mathrm{\bf{\orange{Verification:-}}}}}}} \ {\huge{\green{\checkmark}}}$

$: \ \mapsto {\mathsf{ \ 8,000 \ \bigg [ \bigg ( 1 + \dfrac{\frac{15}{2}}{100} \bigg ) ^{1 \times 2} - 1 \bigg ] = 9,165}}$

$: \ \mapsto {\mathsf{ \ 8,000 \ \bigg [ \bigg ( 1 + \dfrac{7.5}{100} \bigg ) ^{2} - 1 \bigg ] = 9,165}}$

$: \ \mapsto {\mathsf{ \ 8,000 \ \bigg [ \bigg ( \dfrac{100 + 7.5}{100} \bigg ) ^{2} - 1 \bigg ] =9,165}}$

$: \ \mapsto {\mathsf{ \ 8,000 \ \bigg [ \bigg ( \dfrac{107.5}{100} \times \dfrac{107.5}{100} \bigg ) - 1 \bigg ] = 9,165}}$

$: \ \mapsto {\mathsf{ \ 8,000 \ \bigg [ \dfrac{11,556.25}{10,000} - 1 \bigg ] = 9,165 }}$

$: \ \mapsto {\mathsf{ \ 8,000 \ \bigg [ \dfrac{11,556.25-100}{10,000} \bigg ] =9,165 }}$

$: \ \mapsto {\mathsf{ \ 8,000 \times \dfrac{11,456.25}{10,000}=9,165}}$

$: \ \mapsto {\mathsf{ \ 0.8 \times 11,456.25 = 9,165}}$

$: \ \mapsto {\mathsf{ \ 9,165 = 9,165}}$

$\Longrightarrow {\bf{LHS=RHS}} \Longleftarrow$

${\mathsf{Hence, Verified}} \ {\large{\green{\checkmark}}}$