Question

if thev amount is 2 1/4 times the sum after two years at compound interest find the rate of interest per annum

Answer 1

Answer:

50%

Step-by-step explanation:

Say ₹100 was invested

so A=2.25*100=₹225

A=P[1+(r/100)]^n

or

225=100[1+(r/100)]^2

so

225/100=[1+r/100)]^2

and

[1+(r/100)]^2=2.25

so

1+(r/100)=√2.25

=1.5

r=50%

Answer 2

Answer:

The required rate of interest per annum is $50$%

Step-by-step explanation:

Concept:

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

Where,

A = amount

P = principal

r = rate of interest

t = time (in years)

Given: The amount is $2\frac{1}{4}$ times the sum after $2$ years at compound interest.

To find: The objective is to find out the rate of interest per annum.

Solution:

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

Here, $A=2\frac{1}{4} P=\frac{9}{4} P$

$t=2$ years

Now apply the formula,

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

⇒$\frac{9}{4} P=P(1+\frac{r}{100} )^{2}$

⇒$\frac{3}{2} =(1+\frac{r}{100} )$

⇒$\frac{r}{100} =\frac{3}{2} -1$

⇒$\frac{r}{100} =\frac{1}{2}$

⇒$x=50$%

Therefore, the required rate of interest per annum is $50$%.

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