Question

3. A certain sum at compound interest amounts to 12,960 in 2 years and 113,176 in 3 years. Find the rate percent per annum.​

Answer 1

Given:—

• Amount in 2 years is Rs. 12,960
• Amount in 3 years is Rs. 13,176

Formula used:—

• → A = P{1 + (R/100)}^T

where,

• A is Amount
• P is Prinicipal
• R is Rate
• And, T is Time

Calculations:

According to the question, we have

The amount in 2 years is Rs. 12,960

A = P{1 + (R/100)}^T

⇒ 12,960 = P{1 + (R/100)}² ----(1)

The amount in 3 years is Rs. 13,176

⇒ 13,176 = P{1 + (R/100)}³ ----(2)

Dividing equation (2) by (1), we get

⇒ (13,176/12,960) = {1 + (R/100)}

⇒ (13,176/12,960) - 1 = (R/100)

⇒ 216/12,960 = R/100

⇒ R = (216/12,960) × 100

⇒ R = 10/6 %

⇒ R = 1⅔%

∴ The rate of interest per annum is 1⅔ .

Hope it helps.

Answer 2

ANSWER:

Given:

• Amount in 2 years = Rs 12,960
• Amount in 3 years = Rs 1,13,176

To Find:

• Rate percent per annum

Solution:

We are given that,

$\implies\sf Amount\:in\:2\:years= Rs 12,960$

And,

$\implies\sf Amount\:in\:3\:years= Rs 1,13,176$

We know that,

$\hookrightarrow\sf Amount=P\left(1+\dfrac{R}{100}\right)^T$

Taking First case,

$\implies\sf Rs\,12,960=P\left(1+\dfrac{R}{100}\right)^2 - - - - -(1)$

Now, we'll take the Second case,

$\implies\sf Rs\,1,13,176=P\left(1+\dfrac{R}{100}\right)^3$

We can re-write it as,

$\implies\sf Rs\,1,13,176=P\left(1+\dfrac{R}{100}\right)^2\left(1+\dfrac{R}{100}\right)$

$\implies\sf Rs\,1,13,176=\left[P\left(1+\dfrac{R}{100}\right)^2\right]\left(1+\dfrac{R}{100}\right)$

Substituting from (1),

$\implies\sf Rs\,1,13,176=\left[P\left(1+\dfrac{R}{100}\right)^2\right]\left(1+\dfrac{R}{100}\right)$

$\implies\sf 1,13,176=12,960\left(1+\dfrac{R}{100}\right)$

$\implies\sf 1,13,176=12,960+\dfrac{12,960R}{100}$

$\implies\sf 1,13,176-12,960=\dfrac{1296R}{10}$

$\implies\sf 100216=\dfrac{1296R}{10}$

$\implies\sf 1002160=1296R$

$\implies\sf R = \dfrac{1002160}{1296}$

Dividing both numerator and denominator by 16,

$\implies\sf R = \dfrac{62635}{81}$

Hence,

$\implies\bf R = 773\dfrac{22}{81}\%$

Therefore, the rate percent per annum is 62635/81 % or (≈)773.27%.

Formula Used:

• $\hookrightarrow\sf Amount=P\left(1+\dfrac{R}{100}\right)^T$