Question

$\begin{gathered}{\Huge{\textsf{\textbf{\underline{\underline{\purple{Question:}}}}}}}\end{gathered}$
~Find the simple interest and Compound Interest on Rs.1000 for 5 years at 10% per annum?​
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● Don't Spam!!
● Don't be Greedy for points!!
● Need full explanation​

Answer 1

$\begin{gathered}{\Huge{\textsf{\textbf{\underline{\underline{\purple{ANSWER:}}}}}}}\end{gathered}$

simple interest = 1000×5×1/100

= 50 ruppes

compound interest =

Answer 2

Answer :-

• The simple interest is Rs 500.
• The compound interest is Rs 610.51.

To find :-

• The simple interest and compound interest on Rs 1000 for 5 years at 10% per annum.

Solution :-

• Let's find the simple interest!

We know that :-

$\underline{\boxed{\sf SI = \dfrac{Principal \times Rate \times Time}{100}}}$

Here,

• Principal = Rs 1000.
• Rate = 10% per annum.
• Time = 5 years.

Hence,

$\tt SI = \dfrac{1000 \times 10 \times 5}{100}$

Cutting off the zeroes,

$\tt SI = \dfrac{10 \times 10 \times 5}{1}$

Now let's multiply the remaining numbers.

$\tt SI = 10 \times 10 \times 5$

Multiplying the numbers,

$\overline{\boxed{\tt SI = Rs \: 500}}$

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• Now before finding the compound interest, let's find the amount!

We know that :-

$\underline{\boxed{\sf A = Principal \left(1 + \dfrac{Rate}{100}\right)^{Time}}}$

Here,

• Principal = Rs 1000.
• Rate = 10% per annum.
• Time = 5 years.

Hence,

$\rm A = 1000 \left(1 + \dfrac{10}{100} \right)^5$

Reducing 10/100 to it's simplest form,

$\rm A = 1000 \left(1 + \dfrac{1}{10}\right)^5$

The LCM of 1 and 10 is 10, so adding the fractions using their denominators,

$\rm A = 1000 \left(\dfrac{1 \times 10 + 1 \times 1}{10}\right)^5$

On simplifying,

$\rm A = 1000 \left(\dfrac{10+1}{10}\right)^5$

Adding the numbers,

$\rm A = 1000 \left(\dfrac{11}{10}\right)^5$

The power here is 5, so removing the brackets and multiplying 11/10 with itself 5 times,

$\rm A = 1000 \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10}$

Multiplying the numbers,

$\rm A = 1000 \times \dfrac{161051}{100000}$

Multiplying 161051/100000 with 1000,

$\rm A = \dfrac{161051000}{100000}$

Dividing 161051000 by 100000,

$\overline{\boxed{\rm A= Rs \: 1610.51}}$

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• Now let's find the compound interest!

We know that :-

$\underline{\boxed{\sf CI = Amount - Principal}}$

Here,

• Amount = Rs 1610.51.
• Principal = Rs 1000.

Hence,

$\boxed{\bf CI = 1610.51 - 1000}$

$\boxed{\bf CI = Rs \: 610.51}$

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Abbreviations used :-

$\sf SI = Simple \: Interest$

$\sf A = Amount$

$\sf CI = Compound \: Interest$