Question

Find the compound interest on Rs.64000 for per 1 year at the rate of 10% p.a. compounded quarterly.​

Answer 1

Given:

• Principle = Rs.64000
• Rate = 10%
• Time = 1 years.

To Find:

• Compound interest = ?

Formula used:

$\\\bigstar{\underline{\boxed{\bf{ \red{A= P\bigg[1 + \dfrac{ {R}}{100} \bigg]^{4n}}}}}}$

$\bigstar{\underline{\boxed{\bf \: \color{blue}{C.I = Amount - Principal}}}}$

Where :

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

Solution:

★ calculating the amount:

$\\ \dashrightarrow {\sf { A = P \bigg( 1 + \dfrac{R}{400} \bigg)^{4n} }}$

$\dashrightarrow {\sf { A = 64000 \bigg(1 + \dfrac{10}{400} \bigg)^{4 \times 1} }}$

$\dashrightarrow {\sf { A = 64000 \bigg(1 + \dfrac{10}{400} \bigg)^{4} }}$

$\dashrightarrow {\sf { A = 64000 \bigg(1 + \cancel\dfrac{10}{400} \bigg)^{4} }}$

$\dashrightarrow {\sf { A = 64000 \bigg(1 + \cancel\dfrac{5}{200} \bigg)^{4} }}$

$\dashrightarrow {\sf { A = 64000 \bigg(1 + \cancel\dfrac{2.5}{100} \bigg)^{4} }}$

$\dashrightarrow {\sf { A = 64000 \bigg(1.025 \bigg)^{4} }}$

$\dashrightarrow {\sf { A = 64000 \times 1.025 \times 1.025 \times 1.025 \times 1.025 }}$

$\dashrightarrow {\sf { A = 64000 \times 1.103812890625}}$

$\dashrightarrow {\sf { Amount = ₹ \; 70644.025 }}$

${\bigstar{\red{\underline {\boxed {\sf{Amount = ₹ \; 70644.025 }}}}}}$

Hence, the amount is ₹ 70644.025

★ compound interest

$\\{\dashrightarrow{\sf{{C.I=A- P}}}}$

${\dashrightarrow{\sf{{C.I=70644.025 - 64000}}}}$

${\dashrightarrow{\sf{C.I=₹ \; 6644.025}}}$

${\bigstar{\red{\underline {\boxed {\sf{C.I=₹ \; 6644.025 }}}}}}$

Hence, the compound interest is ₹ 6644.025

Answer 2

To find:

$\to$ The compound interest

Given:

• Principle=64000rs
• Time=1year

Solution:

Using formula:

$\to \boxed{\mathsf{Compound \ interest=Principle(1+\frac{Rate \ of \ interest \ per \ annum}{100}) - Principle}}^ \mathsf{Time \ (Number \ of \ years)}$

Using the formula of compund interest finding the compund interest,

$\to \mathsf{64000(1+\frac{10}{100}) ^ \mathsf{1}-64000} \mathsf{rs}\\\\\to =\mathsf{64000(\frac{11}{10} )-64000 rs}\\\\\to =\mathsf{70400-64000rs}\\\\\to = \mathsf{6400rs}$

Answer:

The compound interest=$\mathsf{6400rs}$