Question

Using C.I. formula, calculate the amount and compound interest on (a) ₹40, 000 for 2 years at 9% p.a. interest being paid annually
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Answer 1

★ Amount = ₹47,524 and Compound Interest = ₹7,524.

Step-by-step explanation

By considering the information provided in the question, we can point it as:

• Principal (P) = ₹40,000
• Time (n) = 2 years
• Rate of interest per annum (R) = 9%

From the given data, we have been asked to calculate the amount (A) and compound interest (C.I.).

So as to find the amount, we will be using the formula,

$\twoheadrightarrow \quad{ \sf\pmb{A = P \bigg(1 + \dfrac{R}{100}\bigg)^{n}}}$

Plugging in the given values,

$\twoheadrightarrow \quad{ \sf{A = 40000 \times \bigg(1 + \dfrac{9}{100} \bigg)^{2} }}$

Simplifying the brackets by summing up the fractions.

$\twoheadrightarrow \quad{ \sf{A=40000\times \bigg(\dfrac{109}{100}\bigg)^{2} }}$

Further simplifying the brackets by squaring the numerator and denominator of the fraction,

$\twoheadrightarrow \quad{ \sf{A = 40000 \times \dfrac{ {(109)}^{2} }{ {(100)}^{2} } }}$

$\twoheadrightarrow \quad{ \sf{A = 40000 \times \dfrac{11881}{10000} }}$

Multiplying the fraction with the number,

$\twoheadrightarrow \quad{ \sf{A = \dfrac{40000 \times 11881}{10000} }}$

Reducing the fraction to its lowest form,

$\twoheadrightarrow \quad{ \sf{A = \dfrac{4\times 11881}{1} }}$

$\twoheadrightarrow \quad{ \sf{A = 4\times 11881}}$

$\twoheadrightarrow \quad \underline{\boxed{ \sf{A = 47524}}}$

Therefore, principal has been amounted to ₹47,524.

As we have found the amount, we need to calculate the compound interest now. Here, we will be using the formula:

$\twoheadrightarrow \quad{ \sf\pmb{C.I. = A - P}}$

Plugging in the values,

$\twoheadrightarrow \quad{ \sf{C.I. = 47524 - 40000}}$

Subtracting the numericals,

$\twoheadrightarrow\quad\underline{\boxed{ \sf{C.I. = 7524}}}$

Therefore, the compound interest is ₹7,524.