Question

Seema invests Rs 5000 compounded yearly.At the end of one year,it amounts to Rs 5200.Calculate:(1)rate of interest (2) C.I. for second year ?

Answer 1

Dear student,

$$\begin{gathered} PrincipalP=Rs5000 \\ Timen=1year \\ AmountA=Rs5200 \\ Now,A=P{\left(1+\frac{R}{100}\right)}^n \\ \Rightarrow 5200=5000{\left(1+\frac{R}{100}\right)}^1 \\ \Rightarrow \frac{5200}{5000}=1+\frac{R}{100} \\ \Rightarrow \frac{52}{50}-1=\frac{R}{100} \\ \Rightarrow \frac{52-50}{50}=\frac{R}{100} \\ \Rightarrow \frac{2\times 100}{50}=R \\ \Rightarrow \boxed{R=4\%p.a} \\ \left(2\right)Now, \\ For2ndyears \\ \Rightarrow A=5000{\left(1+\frac{4}{100}\right)}^2 \\ \Rightarrow A=5000{\left(1+\frac{1}{25}\right)}^2 \\ \Rightarrow A=5000\times \frac{26}{25}\times \frac{26}{25} \\ \Rightarrow A=200\times \frac{26}{1}\times \frac{26}{25} \\ \Rightarrow A=8\times 26\times 26 \\ \Rightarrow A=Rs5,408 \\ CI=A-P \\ \Rightarrow CI=5408-5000 \\ \Rightarrow CI=Rs408 \end{gathered}$$

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