Question

At what rate percent of compound interest will 625ruppes become 784 in 2 year

Answer 1

AnswEr :

• Amount = Rs. 784
• Principal = Rs. 625
• Time = 2 Years
• Rate = ? if, compounded yearly

$\leadsto \sf{Amount = P \times \bigg(1 + \dfrac{r}{100} \bigg)^{t} }$

• Plugging the Values

$\leadsto \sf{784 = 625 \times \bigg(1 + \dfrac{r}{100} \bigg)^{2} }$

$\leadsto \sf{ \dfrac{784}{625} = \bigg(1 + \dfrac{r}{100} \bigg)^{2} }$

$\leadsto \sf{ \sqrt{\dfrac{784}{625}} =1 + \dfrac{r}{100} }$

$\leadsto \sf{ \sqrt{\dfrac{28 \times 28}{25 \times 25}} =1 + \dfrac{r}{100} }$

$\leadsto \sf{\dfrac{28}{25} =1 + \dfrac{r}{100} }$

$\leadsto \sf{\dfrac{28}{25} - 1= \dfrac{r}{100} }$

$\leadsto \sf{\dfrac{(28 - 25)}{ \cancel{25}} = \dfrac{r}{ \cancel{100}} }$

$\leadsto \sf{3=\dfrac{r}{4} }$

$\leadsto \sf{r = 4 \times 3}$

$\leadsto \sf{r = 12\%}$

⠀

$\therefore$ Rate of Interest is 12% per annum.