Question

The compound interest on rupees 30,000 at 7% per annum for a certain time is rupees 4347. Find the time period if the interest is compound annually.​

Answer 1

Answer:

2yrs

Step-by-step explanation:

Principal=Rs 30,000

C.I=Rs 4347

Rate of interest=7 %

Amount=Principal+C.I

Amount=30,000+4347=34347Rs.

Let the time is T years' then

⇒34347=30000(1+7/100)^T

⇒34347=30000*(100/107)^T

⇒( 100/107) ^T = 30000/34347

⇒( 100/107) ^T= 10000/11449

⇒( 100/107 )^T =(100/107)^2

∴T=2years.

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Answer 2

Answer:

The time period will be 2 years.

Step-by-step explanation:

In context to the question asked,

We have to find the time period,

As per data given in the question,

We have,

Principal ( P ) = Rs. $30000$,

Rate ( R ) = $7$%

Compound interest ( C. I ) = Rs. $4347$

For calculating the time period,

We have to apply the formula of compound interest,

$A = P\left(1+\frac{r}{100}\right)^{n}$

Let ' t ' be the time period.

Now the amount after t years will be

=> $A = P + C.I$

=> $30,000 + 4347$

=> $Rs. 34,347$

Now, by using the formula:

$\Rightarrow 34,347=30,000\left(1+\frac{7}{100}\right)^{t}$

Dividing both sides of the above equation by $30000$:

$\Rightarrow \frac{34347}{30000}=\left(1+\frac{7}{100}\right)^{t}$

$\Rightarrow \frac{11449}{10000}=\left(\frac{107}{100}\right)^{t}$

$\Rightarrow\left(\frac{107}{100}\right)^{2}=\left(\frac{107}{100}\right)^{t}$

By comparing the power on both sides,

=> t = $2$ years

So, the time period will be $2$ years.