Question

After what time will rs 5400 yield rs 1373 .76 as c.i at 12%per annum

Answer 1

Correct question :

After what time will Rs 5400 yield Rs. 6773.76 as c.i at 12% per annum compounded annually ?

Answer :

❍ n = 2

Given :

Amount ( A ) = Rs. 6773.76

P = Rs. 5400

R = 12 %

Formula should be used :

A = P ( 1 + R / 100 )^n

According to the question :

=> 6773.76 = 5400 ( 1 + 12 / 100 )^n

=> 6773.76 / 5400 = ( 100 + 12 / 100 )^n

=> 1.2544 = ( 112 / 100 )^n

=> 1.2544 = ( 28 / 25 )^n

=> 1.2544 / 10000 = ( 28 / 25 )^n

=> ( 28 / 25 )^2 = ( 28 / 25 )^n

= [ cancelling ( 28 / 25 ) = ( 28 / 25 ) ]

=> n = 2

Removing point :

I have removed point by,

1.2544 = count the digits after point ( . )

=> 4 digits = 4 zeroes ( 10000 )

❥ So It's Done ❥ !!

Answer 2

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• Principal = Rs. 5400

• Compound Interest = Rs. 1373.76

• Rate = 12%

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• Time = ?

$\bf\underline{\underline{\green{Solution:-}}}$

To calculate the time, first we need to find the Amount.

Principal = Rs. 5400

Compound Interest = 1373.76

As we know that:-

$\rm Amount = Principal + Compound \: Interest$

$\rm = 5400 + 1373.76$

$\rm = 6773.76$

$\rm \therefore \underline{ \: \: \underline{ \: \: \pink{Amount= Rs. 6773.76 \: \:} } \: \: }$

Now, the formula used for finding Amount is:-

$\boxed{ \rm \leadsto Amount = P \bigg(1 + \frac{r}{100} \bigg) ^{n} }$

Here:-

• Amount = Rs. 6773.76

• P = Principal = Rs. 5400

• r = rate = 12%

• n = time = ?

$\rm \implies 6773.76= 5400\bigg(1 + \dfrac{12}{100} \bigg) ^{n}$

$\rm \implies 6773.76= 5400\bigg(\dfrac{100+12}{100} \bigg) ^{n}$

$\rm \implies \dfrac{6773.76}{5400}= \bigg(\dfrac{112}{100} \bigg)^{n}$

$\rm \implies 1.2544 = (1.12 )^{n}$

$\rm \implies 1.12\times 1.12 = (1.12 )^{n}$

$\rm \implies (1.12 )^{2} = (1.12 )^{n}$

$\rm \implies n = 2$

$\underline{\boxed{\boxed{\purple{\rm \therefore Time = 2 \: years}}}}$