Question

Mohit borrowed a certain sum at 5% per annum compound interest and cleared this loan by paying Rs. 12,600 at the end of the first year and Rs. 17,640 at the end of the second year. Find the sum borrowed.

Answer 1

For the payment of Rs. 12,600 at the end of first year :
A = Rs. 12,600; n = 1 year and r = 5%

Now, `"A" = "P"( 1 + r/100 )^n`

⇒ 12,600 = `"P"( 1 + 5/100 )^1`

⇒ 12,600 = `"P"(21/20)`

⇒ P = `20/21 xx 12,600 = Rs. 12,000`

For the payment of Rs. 17,640 at the end of second year :
A = Rs. 17,640, n = 2 years and r = 5%

Now, A = `"P"( 1 + r/100 )^n`

⇒ 17,640 = `"P"( 1 + 5/100 )^2`

⇒ 17,640 = `"P"(21/20)^2`

⇒ P = `20/21 xx 20/21 xx 17,640 = Rs. 16,000`

∴ Sum borrowed = Rs. (12,000 + 16,000 ) = Rs. 28,000.