Question

On What sum of money will the difference between the compound interest and simple
interest for 3 years be equal to 930, if the rate of interest charged for both is 10% p.a.?

Answer 1

Given:

Difference between the compound interest and simple  interest for 3 years be equal to 930, if the rate of interest charged for both is 10% p.a.

To Find:

What is sum of money?

Solution:

Let Sum of money is given below:

Sum = P

Time (T) = 3 years

Rate of interest(R) = 10 %

Simple interest will be:

$\mathbf{S.I =\dfrac{PRT}{100}}$

So:

$\mathbf{S.I =\dfrac{P\times 10\times 3}{100}}$

$\mathbf{S.I =\dfrac{3P}{10}}$        ...1)

Compound interest will be:

$\mathbf{C.I =P\left ( \left ( 1+\frac{R}{100} \right )^{T}-1 \right )}$

On putting respective value:

$\mathbf{C.I =P\left ( \left ( 1+\frac{10}{100} \right )^{3}-1 \right )}$

On simplify:

$\mathbf{C.I =P\left ( \left \dfrac{1331}{1000}-1 \right )}$

$\mathbf{C.I =\dfrac{331P}{1000}}$            ...2)

Given that:

C.I - S.I = 930

$\mathbf{\dfrac{331P}{1000}-\dfrac{3P}{10}=930}$

On solving, we get:

P = 30000 Rupees

Means amount of sum is 30000 Rupees.

Answer 2

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Amount of sum is 30000 Rupees.