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please answer the questions please and explain it also! if you want brainlist so answer questions please!for 15 points.​​

Answer»

Answer:

12%

Step-by-step EXPLANATION:

{\underline{{\text{Given}}}}

Principal(P) = RS 5000

Time(t) = 2 yr

Difference between the Simple Interest(S.I) and

Compound Interest(C.I) = Rs 72

{\underline{{\text{To Find:}}}}

Rate of interest(R)

{\underline{{\text{Solution:}}}}

Let, the rate of interest be x % PER annum.

In Case of Simple Interest,

\text{S.I} = \dfrac{ Prt }{100} \\ \\ = \frac{5000 \times x \times 2}{100} \\ \\ = 50x \times 2 \\ \\ = 100x

In Case of Compound Interest,

C.I = P \{(1 + \frac{r}{100})^t-1\}\\ \\ = 5000\{(1 + \frac{x}{100})^2-1 \} \\ \\ = 5000(1 + \frac{x}{100} + 1)(1 + \frac{x}{100} - 1) \: [\text{using (a+b)(a-b)} = {a}^{2} - {b}^{2} ] \\ \\ = 5000(2 + \frac{x}{100} )( \frac{x}{100} ) \\ \\ = 50x(2 + \frac{x}{100} ) \\ \\ = 100x + \frac{50 {x}^{2} }{100} \\ \\ = 100x + \frac{ {x}^{2} }{2}

According to question,

C.I - S.I

\implies (100x + \frac{ {x}^{2} }{2} ) - (100x) = 72 \\ \\ \implies100x - 100x + \frac{ {x}^{2} }{2} = 72 \\ \\ \implies \frac{ {x}^{2} }{2} = 72 \\ \\ \implies{x}^{2} = 144 \\ \\ \implies {x}^{2} = {12}^{2} \\ \\ \implies x = 12

Hence, The required rate of interest is 12% per

annum.

{\underline{{\text{Formula for Interest }}}}

\text{S.I }= \dfrac{Prt}{100}

Where,

P = Principal

r = rate of interest

t = time

S.I = Simple Interest

\text{C.I} = P \{{(1 + \dfrac{r}{100})}^{t} - 1 \}

C.I = Compound Interest


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