Question

1. Calculate the amount and compound interest on: b. 36,400 for 2 years at 6 % per annum compounded annually. If only​

Answer 1

Answer:

Given :

• Principle = Rs.36400
• Rate = 6% p.a.c.a
• Time = 2 years

$\begin{gathered}\end{gathered}$

To Find :

• Amount
• Compound Interest

$\begin{gathered}\end{gathered}$

Using Formulas :

$\longrightarrow{\small{\boxed{\sf{A= P\bigg[1 + \dfrac{ {R}}{100} \bigg]^{T}}}}}$

$\longrightarrow{\small{\boxed{\sf{{C.I=A- P}}}}}$

Where :

• A = Amount
• P = Principle
• R = Rate
• T = Time
• C.I = Compound Interest

$\begin{gathered}\end{gathered}$

Solution :

Finding the compound interest by substituting the values in the formula :

${\implies{\sf{A= P\bigg[1 + \dfrac{ {R}}{100} \bigg]^{T}}}}$

${\implies{\sf{A= 36400\bigg[1 + \dfrac{6}{100} \bigg]^{2}}}}$

${\implies{\sf{A= 36400\bigg[\dfrac{(1 \times 100) + (6 \times 1)}{100} \bigg]^{2}}}}$

${\implies{\sf{A= 36400\bigg[\dfrac{100 + 6}{100} \bigg]^{2}}}}$

${\implies{\sf{A= 36400\bigg[ \: \dfrac{106}{100} \: \bigg]^{2}}}}$

${\implies{\sf{A= 36400\bigg[ \dfrac{106}{100} \times \dfrac{106}{100} \bigg]}}}$

${\implies{\sf{A= 36400\bigg[ \dfrac{106 \times 106}{100 \times 100} \bigg]}}}$

${\implies{\sf{A= 36400\bigg[ \dfrac{11236}{10000} \bigg]}}}$

${\implies{\sf{A= 36400 \times \dfrac{11236}{10000}}}}$

${\implies{\sf{A= 36400 \times \cancel{\dfrac{11236}{10000}}}}}$

${\implies{\sf{A= 36400 \times 1.1236}}}$

${\implies{\sf{\red{A= Rs. \: 40899.04}}}}$

Hence, the amount is Rs.40899.04.

$\rule{190}1$

Now, finding the compound interest by substituting the values in the formula :

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

${\implies{\sf{{C.I=40899.04 - 36400}}}}$

${\implies{\sf{\red{C.I=Rs.4499.04}}}}$

Hence, the compound interest is Rs.4499.04.

$\begin{gathered}\end{gathered}$

Learn More :

$\longrightarrow\small{\underline{\boxed{\sf{ Simple \: Interest = \dfrac{P \times R \times T}{100}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Amount = Principle + Interest}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{ Principle=Amount - Interest }}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Time = \dfrac{Simple \: Interest \times 100}{Principle \times Rate}}}}}$

${\rule{220pt}{2.5pt}}$