A certain sum amounts to 5832 in 2 years at 8 if the interest is compounded annually find the sum

Correct Option: A

Here , P = ? , A = ₹ 5,832 , R = 8%, T = 2 years
Using the given formula ,

A = P		1 +	R		T
100

5832 = P		1 +	8		2
100

⇒  5832 = P		1 +	2		2
25

A certain sum amounts to Rs 5832 in 2 years at 8% compounded interest. Find the sum.

Solution

Let the sum be P . 
Thus, we have: 
\[A = P \left( 1 + \frac{R}{100} \right)^n \]
\[5, 832 = P \left( 1 + \frac{8}{100} \right)^2 \]
\[5, 832 = 1 . 1664P\]
\[P = \frac{5, 832}{1 . 1664}\]
\[ = 5, 000\]
Thus, the required sum is Rs 5, 000.

Q. A certain sum amounts to 5832 Rs. in 2 years at 8% per annum compound interest, the sum is:
Answer: [A] Rs. 5000
Notes: $ 5832 = P \left ( 1+\frac{8}{100} \right )^{2}$ $ => 5832 = P \left ( 1+\frac{2}{25} \right )^{2}$ $ => 5832 = P\times \frac{27}{25}\times \frac{27}{25}$ $ => P = \frac{5832\times 25\times 25}{27\times 27} = 5000 Rs.$ Hence option [A] is correct answer.

 3

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