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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.
Solution
Let Rs. X be the sum.
Simple Interest (I) = `[ "X" xx 8 xx 2]/100` = 0.16X
Compound interest
For 1st 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 2nd 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.
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