Question

a sum compounded annually 25/16times of itself in two years determine the rate of interest per annum?​

Answer 1

Let Principal be x .

then Amount will be =  $\frac{25}{16} x$

Time period = 2 years

We have to calculate rate of interest.

Using formula for compound interest

$A=P(1+\frac{r}{100})^t$

Substitute, we have,

$\frac{25}{16}x=x(1+\frac{r}{100})^2$

Solve, we have,

$\frac{25}{16}=(1+\frac{r}{100})^2$

Taking square root both side, we have,

$\frac{5}{4}=1+\frac{r}{100}$

Solve for r, we have,

$(\frac{5}{4}-1)\times 100=r$

Thus, r = 25%

Thus, Rate of interest per annum is 25%.

Answer 2

$</p><p>\huge {\fbox {\fbox {\rightarrow {\mathfrak {\green {Answer \: : 25 \: Percent.}}}}}}$

Let the Principal Sum Be P.

Therefore, Amount = 25/16 P.

The Time Period Is 2 Years.

$</p><p>\huge {\fbox {\fbox {\rightarrow {\tt {\orange {The \:Formula \:Used \:Is \: -}}}}}}$

$</p><p>\tt{\red {\boxed {\boxed{\rightarrow {A ={ P(1 + \frac{r}{100} )}^{T}}}}}}$

Substituting The Value And Solving We Get The Value Of R as 25%.