# The Difference in Simple Interest and Compound Interest on a Certain Sum of Money at 6 2 3 per Annum for 3 Years is Rs 46. Determine the Sum. - Mathematics

Sum

The difference in simple interest and compound interest on a certain sum of money at $6\frac{2}{3} %$ per annum for 3 years is Rs 46. Determine the sum.

#### Solution

Given:
CI - SI = 46
$P\left[ \left( 1 + \frac{R}{100} \right)^n - 1 \right] - \frac{PRT}{100} = 46$
$P\left[ \left( 1 + \frac{20}{300} \right)^3 - 1 \right] - \frac{P \times 20 \times 3}{3 \times 100} = 46$
$\frac{4, 096}{3, 375}P - \frac{P}{5} - P = 46$
$\frac{(4, 096 - 3, 375 - 675)P}{3, 375} = 46$
$P = 46 \times \frac{3, 375}{46}$
$= 3, 375$
Thus, the required sum is Rs 3, 375 .

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 14 Compound Interest
Exercise 14.3 | Q 20 | Page 21