Question

p=12500 r=12%p.a n=2years compounded anually find amount and compund interest using formula​

Answer 1

Answer:

Amount = Rs. 15680

Compound Interest = Rs. 3180

Step-by-step explanation:

As per the provided information in the given question, we have :

• Principal (P) = Rs. 12500
• Rate (R) = 12%
• Time (n years) = 2 years

We've been asked to calculate amount and compound interest.

As we know that, when the compound interest is compounded annually, then Amount is given by,

$\bigstar \quad\underline{\boxed{\pmb{\frak{A}} = {\pmb{\frak{P}} \Bigg \lgroup \pmb{\frak{1}} + \dfrac{\pmb{\frak{R}}}{\pmb{\frak{100}}} \Bigg \rgroup}^{\pmb{\frak{n}}} }}$

• A denotes amount
• P denotes principal
• R denotes rate
• n denotes time

Substitute the values in the formula.

$\twoheadrightarrow \frak{\quad { A = 12500 { \Bigg \lgroup 1 + \dfrac{12}{100} \Bigg \rgroup }^{2} }}$

Taking the LCM and performing addition in the brackets in the RHS.

$\twoheadrightarrow \frak{\quad { A = 12500 { \Bigg \lgroup \dfrac{100 + 12}{100} \Bigg \rgroup }^{2} }}$

Performing addition in the numerator of the fraction in the brackets in RHS.

$\twoheadrightarrow \frak{\quad { A = 12500 { \Bigg \lgroup \dfrac{112}{100} \Bigg \rgroup }^{2} }}$

Rearranging the terms and simplifying further.

$\twoheadrightarrow \frak{\quad { A = 12500 \times \cancel{\dfrac{112}{100}} \times\cancel{ \dfrac{112}{100} }}}$

Reducing the fractions to their lowest terms.

$\twoheadrightarrow \frak{\quad { A = \cancel{12500} \times \dfrac{28}{\cancel{25}} \times \dfrac{28}{25} }}$

Dividing 125000 by 25.

$\twoheadrightarrow \frak{\quad { A = 500 \times 28 \times \dfrac{28}{25} }}$

Dividing 125000 by 25, once again.

$\twoheadrightarrow \frak{\quad { A = 20 \times 28 \times 28 }}$

Performing the multiplication of the terms.

$\twoheadrightarrow \quad\underline{\boxed {\pmb{\frak{ A = Rs. \; 15680}} }}$

Now, we have to calculate compound interest. As we know that,

$\bigstar \quad \underline{\boxed{\pmb{\frak{C.I}} = \pmb{\frak{Amount - Principal}} }}$

Substitute the values.

$\twoheadrightarrow \frak{\quad { C.I = Rs. \; ( 15680 - 12500) }}$

Performing subtraction of the terms.

$\twoheadrightarrow \quad\underline{\boxed {\pmb{\frak{ C.I = Rs. \; 3180}} }}$

⠀⠀_______________________________⠀⠀⠀⠀

• Amount = Rs. 15680
• Compound Interest = Rs. 3180

❝ Therefore, amount is Rs. 15680 and compound interest is Rs. 3180. ❞