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.

Answer 1

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.