Question

find the compound interest on a sum of RS 12000 at the rate of 8% per annum for 1 year compounded quarterly. please step by step ​

Answer 1

Compound interest

When the interest accumulated from time to time till now is calculated in the principal amount, then it is called compound interest.

Compound interest CI received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is as follows:

$\boxed{\:\sf{CI = P {\bigg[1 + \dfrac{R}{400} \bigg]}^{4n} - P\:}}$

Where,

• CI - Compund Interest
• P - Principal Amount
• R - Rate of Interest
• n - Time Period.

As per the provided information in the given question, we have been given that,

• Principal amount, P = Rs. 12000
• Rate of interest, R = 8% per annum
• Time period, n = 1 year
• Compound interest, CI = ?

Solution:

By substituting the given values in the formula, we get the following results:

$CI = P{\bigg[1 + \dfrac{R}{400} \bigg]}^{4n} - P$

$\implies CI = 12000 {\bigg[1 + \dfrac{8}{400} \bigg]}^{4\times1} - 12000$

$\implies CI = 12000 {\bigg[1 + \cancel{\dfrac{8}{400}} \bigg]}^{4} - 12000$

$\implies CI = 12000 {\bigg[1 + \dfrac{1}{50} \bigg]}^{4} - 12000$

$\implies CI = 12000 {\bigg[ \dfrac{50 + 1}{50} \bigg]}^{4} - 12000$

$\implies CI = 12000 {\bigg[ \dfrac{51}{50} \bigg]}^{4} - 12000$

$\implies CI = 12000 \times \dfrac{51^4}{50^4} - 12000$

$\implies CI = 12\cancel{000} \times \dfrac{6765201}{6250\cancel{000}} - 12000$

$\implies CI = \cancel{12} \times \dfrac{6765201}{\cancel{6250}} - 12000$

$\implies CI = 0.00192 \times 6765201 - 12000$

$\implies CI = 12989.18 - 12000$

$\implies CI = 12989.18 - 12000$

$\implies \boxed{\textsf{\textbf{CI = 989.1859}}}$

Therefore, the compound interest is Rs. 989.1859.

Answer 2

$\\ \large{\underline{\underline{\maltese{\red{\pmb{\sf{ \; Given \; :- }}}}}}}$

• Principal = 12000
• Rate = 8 %
• Time = 1 year
• Compounded = Quarterly

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$\\ \large{\underline{\underline{\maltese{\color{darkblue}{\pmb{\sf{ \; To \; Find \; :- }}}}}}}$

• Compound Interest = ?

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$\\ \large{\underline{\underline{\maltese{\color{maroon}{\pmb{\sf{ \; Solution \; :- }}}}}}}$

⚝ Formula Used :

• Amount :

${\pink{\star}} \; {\pmb{\underline{\overline{\boxed{\orange{\sf{ Amount = Principal \bigg\{ 1 + \dfrac{Rate}{400} \bigg\}^{4 \times Time} }}}}}}} \; {\pink{\star}}$

• Compound Interest :

${\pink{\star}} \; {\pmb{\underline{\overline{\boxed{\orange{\sf{ Compound \; Interest = Amount - Principal }}}}}}} \; {\pink{\star}}$

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⚝ Calculating the Amount :

${\longmapsto{\qquad{\sf{ Amount = Principal \bigg\{ 1 + \dfrac{Rate}{400} \bigg\}^{4 \times Time} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \bigg\{ 1 + \dfrac{8}{400} \bigg\}^{4 \times 1} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \bigg\{ 1 + \dfrac{8}{400} \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \bigg\{ 1 + \cancel\dfrac{8}{400} \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \bigg\{ 1 + \cancel\dfrac{4}{200} \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \bigg\{ 1 + \cancel\dfrac{2}{100} \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \bigg\{ 1 + 0.02 \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \bigg\{ 1.02 \bigg\}^{4} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \times 1.02 \times 1.02 \times 1.02 \times 1.02 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 12000 \times 1.08243216 }}}} \\ \\ \ {\qquad \; \; \; \; {\therefore \; {\underline{\boxed{\pmb{\green{\sf{ Amount = ₹ \; 12989.185 }}}}}}}}$

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⚝ Calculating the Compound Interest :

${\implies{\qquad{\sf{ Compound \; Interest = Amount - Principal }}}} \\ \\ \ {\implies{\qquad{\sf{ Compound \; Interest = 12989.185 - 12000 }}}} \\ \\ \ {\qquad \; \; \; \; {\therefore \; {\underline{\boxed{\pmb{\red{\sf{Compound \; Interst = ₹ \; 989.185 }}}}}}}}$

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⚝ Therefore :

❛❛ Compound Interest on this sum of money is ₹ 989.185 . ❜❜

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