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Question
Mr. Sharma borrowed a certain sum of money at 10% per annum compounded annually. If by paying Rs.19,360 at the end of the second year and Rs. 31,944 at the end of the third year he clears the debt; find the sum borrowed by him.
Solution
At the end of the two years the amount is
`"A"_1 = "P"( 1 + r/100 )^n`
⇒ `"A"_1 = "P"( 1 + 10/100 )^2`
Mr. Sharma paid Rs. 19,360 at the end of the second year.
So for the third year the principal is A1 - 19,360.
Also, he cleared the debt by paying Rs. 31,944 at the end of the third year.
`"A"_2 = "P"( 1 + r/100 )^n`
⇒ 31,944 = `("P"( 1 + 10/100 )^2 - 19,360)( 1 + 10/100)^1`
⇒ 29040 = `("P"( 1 + 10/100 )^2 - 19,360)`
⇒ `"P"( 1 + 10/100 )^2 = 48,400`
⇒ P = Rs. 40,000
Mr. Sharma borrowed Rs. 40,000.
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