Question

Find the amount and compound interest on a sum of rupees 15625 at 4% per annum for 3 years compound Half - yearly .​

Answer 1

Given :

• Principal = Rs.15625
• Rate = 4 %
• Time = 3 years
• Compounded = Half - yearly

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

To Find :

• Compound Interest = ?
• Amount = ?

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

Solution :

$\dag \; {\underline{\pmb{\frak{ Formula \; Used \; :- }}}}$

• ${\underline{\boxed{\red{\sf{ A = P \bigg\lgroup 1 + \dfrac{R}{200} \bigg\rgroup ^{2n} }}}}}$

• ${\underline{\boxed{\red{\sf{ C.I = Amount - Principal }}}}}$

Where :

• ➟ A = Amount
• ➟ C.I = Compound Interest
• ➟ P = Principal
• ➟ R = Rate
• ➟ n = Time

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

$\dag \; {\underline{\pmb{\frak{ Calculating \; the \; Amount \; :- }}}}$

$:\longmapsto{\qquad{\sf{ A = P \bigg\lgroup 1 + \dfrac{R}{200} \bigg\rgroup ^{2n} }}} \\ \\ \ :\longmapsto{\qquad{\sf{ A = 15625 \bigg\lgroup 1 + \dfrac{4}{200} \bigg\rgroup ^{2 \times 3} }}} \\ \\ \ :\longmapsto{\qquad{\sf{ A = 15625 \bigg\lgroup 1 + \dfrac{4}{200} \bigg\rgroup ^{6} }}} \\ \\ \ :\longmapsto{\qquad{\sf{ A = 15625 \bigg\lgroup 1 + \cancel\dfrac{4}{200} \bigg\rgroup ^{6} }}} \\ \\ \ :\longmapsto{\qquad{\sf{ A = 15625 \bigg\lgroup 1 + \cancel\dfrac{2}{100} \bigg\rgroup ^{6} }}} \\ \\ \ :\longmapsto{\qquad{\sf{ A = 15625 \bigg\lgroup 1 + 0.02 \bigg\rgroup ^{6} }}} \\ \\ \ :\longmapsto{\qquad{\sf{ A = 15625 \bigg\lgroup 1.02 \bigg\rgroup ^{6} }}} \\ \\ \ :\longmapsto{\qquad{\sf{ A = 15625 \times 1.06 \times 1.06 \times 1.06 \times 1.06 \times 1.06 \times 1.06 }}} \\ \\ \ :\longmapsto{\qquad{\sf{ A = 15625 \times 1.418519112256 }}} \\ \\ \ {\qquad{\green{\pmb{\sf{ Amount = ₹ \; 22164.36 }}}}}$

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

$\dag \; {\underline{\pmb{\frak{ Calculating \; the \; Compound \; Interest \; :- }}}}$

${\dashrightarrow{\qquad{\sf{ Compound \; Interest = Amount - Principal }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Compound \; Interest = 22164.36 - 15625 }}}} \\ \\ \ {\qquad{\orange{\pmb{\sf{ Compound \; Interest = ₹ \; 6539.36 }}}}}$

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

$\dag \; {\underline{\pmb{\frak{ Therefore \; :- }}}}$

❛❛ Compound Interest on this sum of money is ₹ 6539.36 . ❜❜

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

Answer 2

Refer the given attachment