Question

Find the sum on which the difference between the simple interest and compound interest at the rate of 8% per annum compounded annually would be Rs. 64 in 2 years.

Answer 1

Let Rs. X be the sum.
Simple Interest (I) = `[ "X" xx 8 xx 2]/100` = 0.16X

Compound interest

For 1^st year :

P = Rs. X, R = 8% and T = 1

⇒ Interest (I) = `["X" xx 8 xx 1]/100` = 0.08X

And amount = ₹(x + 0.08x)

=  ₹1.08x

For 2^nd year :

P = Rs. X + Rs. 0.08X = Rs.1.08X

⇒ Interest (I) = `["1.08X" xx 8 xx 1]/100` = 0.0864X

And, amount = ₹(1.08x + 0.0864x)

= ₹1.1664x

So,
C.I  = Amount - p

= ₹(1.1664 x - x)

= ₹ 0.1664x 

The difference between the simple interest and compound interest at the rate of 8% per annum compounded annually should be Rs. 64 in 2 years.

₹0.1664x - ₹0.16x = ₹64

₹0.0064x = ₹64

x = ₹10000

Therefore, the sum is ₹10,000.