Question

The compound interest on a sum of money for two years is Rs 26 and thesimple interest for two years at the same rate is Rs.25. What is the rate of interest ?

Answer 1

$\textbf{Given:}$

$\text{Compound interest = Rs.26}$

$\text{simple interest = Rs.25}$

$\textbf{To find: Rate of interest}$

$\text{By using simple interest formula}$

$\textbf{Simple interest= \bf\frac{Pnr}{100} }$

$\frac{P(2)r}{100}=25$

$\frac{Pr}{50}=25$

$\implies\bf\,Pr=1250$

$\text{By using compund interest formula}$

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

$P(1+\frac{r}{100})^n-P=26$

$P(1+\frac{r}{100})^2-P=26$

$P(1+\frac{r^2}{10000}+\frac{2r}{100})-P=26$

$P(1+\frac{r^2}{10000}+\frac{r}{50})-P=26$

$P+\frac{Pr^2}{10000}+\frac{Pr}{50}-P=26$

$\frac{Pr^2}{10000}+\frac{Pr}{50}=26$

$\frac{1250r}{10000}+\frac{1250}{50}=26$

$\frac{r}{8}+25=26$

$\frac{r}{8}=1$

$\implies\bf\,r=8%$

$\therefore\textbf{The rate of interest is 8 per cent}$

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Answer 2

The rate of interest is 8%.

Step 1: Given data

The Compound Interest = Rs 26  ( for 2 years)

The Simple Interest      = Rs 25 ( for 2 years)

Step 2: To find

we have to find the rate of interest R = ?

Step 3: Formula used

Simple Interest              $=\frac{PNR}{100}$

Compound Interest      = $P( 1 + \frac{r}{100} )^{n} -P$

In S.I  number of years is 2. Hence N= 2

$\frac{PNR}{100} =25$

$\frac{P(2)R}{100} =25$  

${P(2)R}{ =2500$

$PR = 1250$

In C. I number of years is 2. Hence N= 2

$P(1+\frac{r}{100})^n-P=26$

$P(1+\frac{r}{100})^2-P=26$

$P(1+\frac{r^2}{10000}+\frac{2r}{100})-P=26$     Using $( a + b)^{2} = a^{2} + b^{2} + 2ab$

$P+\frac{Pr^2}{10000}+\frac{Pr}{50}-P=26$

Substitute the value pr = 1250.

$\frac{Pr^2}{10000}+\frac{Pr}{50}=26$  

$\frac{1250r}{10000}+\frac{1250}{50}=26$

$\frac{r}{8}+25=26$

$\frac{r}{8}=26 -25$

$\frac{r}{8}=1$

so, r = 8%

Hence the rate of interest is 8%.

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