Question

Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same
period is?

Answer 1

Answer :-

• The compound interest on the same sum for the same period is Rs 81.6.

Given :-

• Simple interest on a sum at 4% per annum for 2 years is Rs 80.

To find :-

• The compound interest on the same sum for the same period.

Step-by-step explanation :-

• In this question, the simple interest, rate and time have been given to us. We first have to find the principal using the information given to us and then use the principal, rate and time to find the compound interest on the same sum for the same period.

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Before finding the compound interest, let's find the principal using the formula of simple interest!

We know that :-

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

Here,

• Simple Interest = Rs 80.
• Rate = 4% per annum.
• Time = 2 years.

• Let the principal be p.

$\underline{ \mathfrak{Substituting \: given \: values \: in \: this \: formula,}}$

$\tt80 = \dfrac{p \times 4 \times 2}{100}$

Multiplying 4 with 2,

$\tt80 = \dfrac{p \times 8}{100}$

Multiplying p with 8,

$\tt80 = \dfrac{8p}{100}$

Transposing 100 from RHS to LHS, changing it's sign,

$\tt80 \times 100 = 8p$

Multiplying 80 with 100,

$\tt8000 = 8p$

Transposing 8 from RHS to LHS, changing it's sign,

$\tt \dfrac{8000}{8} = p$

Dividing 8000 by 8,

$\overline{\boxed{\tt Rs \: 1000 = p}}$

• The principal is Rs 1000.

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Now we know the principal, so let's find the compound interest on the same sum for the same period!

For finding the compound interest, we first have to find the amount!

We know that :-

$\underline{\boxed{\sf Amount = Principal \Bigg(1 + \dfrac{Rate}{100} \Bigg)^{Time}}}$

Here,

• Principal = Rs 1000.
• Rate = 4% p.a.
• Time = 2 years.

$\underline{ \mathfrak{Substituting \: given \: values \: in \: this \: formula,}}$

$\rm Amount = 1000 \Bigg(1 + \dfrac{4}{100} \Bigg)^{2}$

Making 1 a fraction by taking 1 as the denominator,

$\rm Amount = 1000 \Bigg( \dfrac{1}{1} + \dfrac{4}{100} \Bigg)^{2}$

The LCM of 1 and 100 is 100, so adding the fractions using their denominators,

$\rm Amount = 1000 \Bigg( \dfrac{1 \times 100 + 4 \times 1}{100} \Bigg)^{2}$

On simplifying,

$\rm Amount = 1000 \Bigg( \dfrac{100 + 4}{100} \Bigg)^{2}$

Adding 4 to 100,

$\rm Amount = 1000 \Bigg( \dfrac{104}{100} \Bigg)^{2}$

The power here is 2, so removing the brackets and multiplying 104/100 with itself 2 times,

$\rm Amount = 1000 \times \dfrac{104}{100} \times \dfrac{104}{100}$

Let's multiply 104/100 with itself first.

$\rm Amount = 1000 \times \dfrac{104 \times 104}{100 \times 100}$

On multiplying,

$\rm Amount = 1\!\!\! \not0 \!\!\!\not0 \!\!\!\not0 \times \dfrac{10816}{10 \!\!\!\not0 \!\!\!\not0 \!\!\!\not0}$

Cutting off the zeroes,

$\rm Amount = 1 \times \dfrac{10816}{10}$

Multiplying 1 with 10816/10,

$\rm Amount = \dfrac{10816}{10}$

Dividing 10816 by 10,

$\overline{ \boxed{\rm Amount = Rs \:1081.6}}$

• The amount is Rs 1081.6.

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Now finally let's find the compound interest!

We know that :-

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

Here,

• Amount = Rs 1081.6.
• Principal = Rs 1000.

$\underline{ \mathfrak{Substituting \: given \: values \: in \: this \: formula,}}$

$\boxed{\bf CI = 1081.6 - 1000}$

Subtracting 1000 from 1081.6,

$\overline{ \boxed{\bf CI = Rs \: 81.6}}$

• Hence, the compound interest is Rs 81.6.

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Abbreviations used :-

$\sf SI = Simple\: Interest.$

$\sf CI = Compound\: Interest.$

Answer 2

Given :

• Simple Interest = Rs 80
• Rate (R) = 4% p.a
• Time (T) = 2 years

To Find :

• Principal
• Compound interest on the same sum for the same time period.

Formulas :

• A = P [1 + R / 100]^n
• CI = A - P
• SI = P × R × T / 100
• P = SI × 100 / R × T

where ,

• P denotes Principal
• R denotes Rate
• n denotes Time
• T denotes Time
• A denotes Amount
• CI denotes Compound Interest
• SI denotes Simple Interest

Solution :

✰ As we know that, for finding the Compound Interest we need Principal, so firstly we will find the principal by using the formula P = SI × 100 / R × T as Simple Interest is given. After finding the Principal we will find the amount and then we will find the Compound interest. Amount will be calculated by using the formula A = P [1 + R / 100]^n and Compound Interest will be given by the formula Compound Interest = Amount - Principal.

⠀⠀⠀

⠀⠀⠀⟼⠀⠀SI = P × R × T / 100

⠀⠀⠀⟼⠀⠀P = SI × 100 / R × T

⠀⠀⠀⟼⠀⠀P = 80 × 100 / 4 × 2

⠀⠀⠀⟼⠀⠀P = 8000 / 8

⠀⠀⠀⟼⠀⠀P = 1000

Thus Principal is Rs 1000

⠀⠀

Now,

⠀⠀⠀⟼⠀⠀A = P [1 + R / 100]^n

⠀⠀⠀⟼⠀⠀A = 1000[1 + 4 / 100]²

⠀⠀⠀⟼⠀⠀A = 1000[104/100]²

⠀⠀⠀⟼⠀⠀A = 1000[26/25]²

⠀⠀⠀⟼⠀⠀A = 1000 × 26/25 × 26/25

⠀⠀⠀⟼⠀⠀A = 40 × 26 × 26/25

⠀⠀⠀⟼⠀⠀A = 40 × 676/25

⠀⠀⠀⟼⠀⠀A = 27,040/25

⠀⠀⠀⟼⠀⠀Amount = Rs 1,081.6

⠀⠀

So,

⠀⟼⠀⠀Compound Interest = A - P

⟼⠀⠀Compound Interest = 1081.6 - 1000

⠀⟼⠀⠀Compound Interest = Rs 81.6

Thus Compound Interest is Rs 81.6

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