Question

The ci on. sum in 8 years is rs.400 and ci on the same sum in 16 years is rs.1300 find ci on the same sum in 20 year​

Answer 1

$\textbf{Given:}$

$\text{8 years compound interest=Rs.400}$

$\text{16 years compound interest=Rs.1300}$

$\textbf{To find:}$

$\text{The compound interest for 20 years}$

$\text{By using compund interest formula}$

$\textbf{Comound interest= \bf\,P(1+\frac{r}{100})^n-P }$

$400=P(1+\frac{r}{100})^8-P$

$P+400=P(1+\frac{r}{100})^8$.....(1)

$\text{and}$

$1300=P(1+\frac{r}{100})^{16}-P$

$P+1300=P(1+\frac{r}{100})^{16}$.....(2)

$\text{Divide (2) by (1)}$

$\dfrac{P+1300}{P+400}=(1+\frac{r}{100})^8$

$\text{Using (1)}$

$\dfrac{P+1300}{P+400}=\dfrac{P+400}{P}$

$P(P+1300)=(P+400)^2$

$P^2+1300\,P=P^2+160000+800\,P$

$1300\,P-800\,P=160000$

$500\,P=160000$

$P=\dfrac{160000}{500}$

$P=\dfrac{1600}{5}$

$\implies\bf\,P=Rs.320$

$\text{Now (1) becomes}$

$320+400=320(1+\frac{r}{100})^8$

$\dfrac{720}{320}=(1+\frac{r}{100})^8$

$\dfrac{9}{4}=(1+\frac{r}{100})^8$

$\text{Taking square root on bothsides, we get}$

$\implies(1+\frac{r}{100})^4=\dfrac{3}{2}$.....(3)

$\text{Now, again using compound interest formula for 20 years}$

$\text{Comound interest= P(1+\frac{r}{100})^{20}-P }$

$\text{Comound interest= 320[(1+\frac{r}{100})^4]^5-320 }$

$\text{Comound interest= 320[\frac{3}{2}]^5-320 }$

$\text{Comound interest= 320[\frac{243}{32}]-320 }$

$\text{Comound interest= 10(243)-320 }$

$\text{Comound interest=Rs. 2110 }$

$\therefore\textbf{Compound interest for 20 years is Rs. 2110}$

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