Question

At what rate percent a sum of 4000 yield a C.I. of 410 in 2 years

Answer 1

$\huge{\underline{\b{Question:}}$

At what rate % a sum of Rs. 4000 yield a CI of Rs. 410 in 2 years ?

$\tt{Solution:}$

Given :

• Principle = Rs. 4000.
• CI = Rs.410.
• Time = 2 years.

Let the rate be r % .

We know that ,

$\boxed{\bold{Amount=Principle+CI=P(1+\dfrac{r}{100})^n}}$

$\implies\bold{4000+410=4000(1+\dfrac{r}{100})^2}\\\\\\\implies\bold{4410=4000(1+\dfrac{r}{100})^2}\\\\\\\implies\bold{\dfrac{4410}{4000}=(1+\dfrac{r}{100})^2}\\\\\\\implies\bold{\dfrac{441}{400}=(1+\dfrac{r}{100})^2}\\\\\\\implies\bold{(\dfrac{21}{20})^2=(1+\dfrac{r}{100})^2}\\\\\\\implies\bold{\dfrac{21}{20}=\dfrac{100+r}{100}}\\\\\\\implies\bold{\dfrac{21*100}{20}=100+r}\\\\\\\implies\bold{21*5=100+r}\\\\\\\implies\bold{r=105-100=5\%.}\\\\\\\boxed{\boxed{\bold{Rate=5\%.}}}$

Answer 2

$\underline{\underline{\mathbf{Heya\:Mate}}}$

$\underline{\bold{Question}}$

At what rate percent a sum of 4000 yield a C.I. of 410 in 2 years ?

$\underline{\bold{Solution}}$

Given :

Principle = Rs.4000

Compound interest = Rs.410

Amount = Rs.4000 + Rs. 410 = Rs.4410

Time = 2 years

rate = ?

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

⇒ Rs.4410 = Rs.4000( 1 + $\frac{r}{100}$ ) ^ 2

⇒ $\frac{4410}{4000}$ = ( 1 + $\frac{r}{100}$ ) ^ 2

⇒ $\frac{441}{400}$ = ( 1 + $\frac{r}{100}$ ) ^ 2.

⇒ $\frac{21 × 21}{20 × 20}$ = ( 1 + $\frac{r}{100}$ ) ^ 2

⇒ $\frac{21}{20}$ = 1 + $\frac{r}{100}$

⇒ $\frac{21}{20}$ - 1 = $\frac{r}{100}$

⇒ $\frac{1}{20}$ = $\frac{r}{100}$

⇒ $\frac{1}{20}$ × 100 = r

⇒ 5 % = r

$\therefore$$<b>$rate is 5%

$<b><u> Hope it helps you </u></b>$