The difference between compound and simple interests on a certain sum of money at the interest rate of 10% per annum for 11/2 years is ₹183, when the interest is compounded semi-annually, then the sum of money is : Option 1: ₹ 22,000 Option 2: ₹ 24,000 Option 3: ₹ 26,000 Option 4: ₹ 28,000

Answer: ₹ 24,000. Solution: Let the sum of money be x. The rate is 10 % per annum, compounded semi-annually, so the rate per half-year is 5%, The number of periods in 1.5 years is 3. Using the compound interest formula: CI = x(1+5/100)^3 -x CI =x(21/20)^3-x CI=x((441 x 21)/8000)-x CI=x(9261/8000)-x CI=x(1261/8000) Now, simple interest: SI = (x * 3 * 5)/100=(15 x)/100=(3 x)/20. The difference between Cl and SI is given as ₹183, so: (1261 x)/8000-(3 x)/20=183 (1261 x-1200 x)/8000=183 (61 x)/8000=183 x=3 x 8000=24,000 Hence, the correct option is Option 2.

Arithmetic

Simple & Compound Interest

Medium

The difference between compound and simple interests on a certain sum of money at the interest rate of $10\%$ per annum for $1\frac{1}{2}$ years is $₹183$ , when the interest is compounded semi-annually, then the sum of money is :

₹ 22,000

₹ 24,000

₹ 26,000

₹ 28,000

✅ Correct Option: 2

Let the sum of money be $x$ .

The rate is $10 \%$ per annum, compounded semi-annually, so the rate per half-year is $5\%$ ,

The number of periods in $1.5$ years is $3$ .

Using the compound interest formula:

$CI =$ $x\left(1+\dfrac{5}{100}\right)^{3} -x$

$CI =x\left(\dfrac{21}{20}\right)^{3}-x$

$CI=x\left(\dfrac{441 \times 21}{8000}\right)-x$

$CI=x\left(\dfrac{9261}{8000}\right)-x$

$CI=x\left(\dfrac{1261}{8000}\right)$

Now, simple interest:

$SI = \dfrac{x \cdot 3 \cdot 5}{100}=\dfrac{15 x}{100}=\dfrac{3 x}{20}$ .

The difference between Cl and SI is given as ₹183, so:

$\Rightarrow \dfrac{1261 x}{8000}-\dfrac{3 x}{20}=183$

$\Rightarrow \dfrac{1261 x-1200 x}{8000}=183$

$\Rightarrow \dfrac{61 x}{8000}=183$

$\Rightarrow x=3 \times 8000=24,000$

Hence, the correct option is Option 2.

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The difference between compound and simple interests on a certain sum of money at the interest rate of $10\%$ per annum for $1\frac{1}{2}$ years is $₹183$ , when the interest is compounded semi-annually, then the sum of money is :