Question

find the sum, if the compound in interest ot 5% for two years compounded annually is ₹ 164​

Answer 1

Answer :

• The sum of money is ₹1600

Given :

• The compound in interest ot 5% for two years compounded annually is ₹ 164

To find :

• Sum of money

Solution :

• Let the sum of money be x (principal)

Given,

• Rate (R) = 5% per annum
• Time(T) = 2 years
• Compound interest (CI) = 164₹

• CI = P(1 + R/100)n - P

Where,

• CI is compound interest
• P is principal
• R is rate
• n is time

Substituting the value :

↦ CI = P(1 + R/100) n - P

↦ 164 = x(1 + 5/100)² - 1

↦ 164 = x(105/100)² - 1

↦ 164 = x((1.05)² - 1)

↦ x = 164/((1.05)² - 1)

↦ x = 164/0.1025

↦ x = 1600₹

Hence

The sum of money is ₹1600.

Answer 2

Question :-

• On what sum will the compound interest at 5 % per annum for 2 years compounded annually be Rs. 164 .

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Answer :-

• Required Sum = Rs. 1600 .

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Explanation :-

• Here, Rate is given 5 % , Compound Interest is given Rs. 164 , Time Period is given 2 years . And, we have to calculate the Sum .

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◆ Formula Required :-

• $\sf{C.I = P \bigg(1 + \frac{R}{100} \bigg) {}^{n} - P }$

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◆ Here ,

• C.I denotes to Compound Interest .
• P denotes to Principal .
• R denotes to Rate .
• N denotes to Time Period .

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∴ By substituting the given values :-

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$\dashrightarrow \: \sf{164 = x \bigg(1 + \frac{5}{100} \bigg) {}^{2} - 1 } \\ \\ \dashrightarrow \: \sf{164 = x \bigg(\frac{105}{100} \bigg) {}^{2} - 1} \\ \\ \dashrightarrow \: \sf{164 = x\bigg( \big[1.05 \big] {}^{2} - 1 \: \bigg) } \\ \\ \dashrightarrow \: \sf{x = 164 \bigg( \big[1.05 \big] {}^{2} - 1\bigg) } \\ \\ \dashrightarrow \: \sf{x = \frac{164}{0.1025} } \\ \\ \dashrightarrow \: \sf{x =Rs. \: 1600 }$

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Hence :-

• Required Sum = Rs. 1600 .

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