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AnswEr:
\bf{ Given}\begin{cases}\sf{Principal = Rs. \:7500}
\sf{Amount = Rs.\:8427}
\sf{Time = 2 \:years}
\sf{Rate = ?\% \:p.a} \end{cases}
• Amount of Compound Interest will be:
\longrightarrow \tt{Amount = P \times \bigg(1+\dfrac{r}{100} \bigg)^{t}}
\longrightarrow \tt{8427 =7500\times \bigg(1 +\dfrac{r}{100} \bigg)^{2}}
\longrightarrow \tt{ \cancel\dfrac{8427}{7500}=\bigg(1 +\dfrac{r}{100}
\bigg)^{2}}
\longrightarrow \tt{\dfrac{2809}{2500}=\bigg(1 +\dfrac{r}{100} \bigg)^{2}}
\longrightarrow \tt{ \sqrt{ \dfrac{2809}{2500}}=1 +\dfrac{r}{100}}
\longrightarrow \tt{ \sqrt{ \dfrac{53 \times 53}{50 \times 50}}=1 +\dfrac{r}{100}}
\longrightarrow \tt{ \dfrac{53}{50}=1 +\dfrac{r}{100}}
\longrightarrow \tt{ \dfrac{53}{50} - 1=\dfrac{r}{100}}
\longrightarrow \tt{ \dfrac{53 - 50}{50}=\dfrac{r}{100}}
\longrightarrow
\tt{ \dfrac{3}{ \cancel{50}}=\dfrac{r}{\cancel{100}}}
\longrightarrow \tt{3 = \dfrac{r}{2} }
\longrightarrow \tt3 \times 2 = r
\longrightarrow \large\boxed{ \red{\tt Rate = 6\% \:p.a.}}
⠀
∴ RateofInterestwillbe6%perannum.
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Present value, P = Rs.7500
Amount, A = Rs.8427
Time, n = 2 years
Now,
Amount (A) = P (1 + R/100)n
⇒ 8427 = 7500 (1 + R/100)2
⇒ (1 + R/100)2 = 8427/7500
⇒ (1 + R/100)2 = (53/50)2
⇒ (1 + R/100) = (53/50)
⇒ R/100 = 53/50 – 1
⇒ R/100 = (53 – 50)/50
⇒ R = 3/50 × 100
⇒ R = 6
∴ Rate = 6%
Present value, P = Rs.7500
Amount, A = Rs.8427
Time, n = 2 years
Now,
Amount (A) = P (1 + R/100)n
⇒ 8427 = 7500 (1 + R/100)2
⇒ (1 + R/100)2 = 8427/7500
⇒ (1 + R/100)2 = (53/50)2
⇒ (1 + R/100) = (53/50)
⇒ R/100 = 53/50 – 1
⇒ R/100 = (53 – 50)/50
⇒ R = 3/50 × 100
⇒ R = 6
∴ Rate = 6%
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Updated On: 27-06-2022
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