Question

If Rs40000 amounts to Rs48620.25 in 2 years,compound interest payable half yearly,Find the rate of interest per annum​

Answer 1

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$\bold\blue{Solution}$

$Principal = 40000$

$Amount = 48620.25$

$Time = 2 years$

$Formula\: of\: amount = A = p(1 + \dfrac{r}{100})^{n}$

$\Rightarrow 48620.25 = 40000(1 + \dfrac{r}{100})^{2}$

$\dfrac{4862025}{4000000} = (1 + \dfrac{r}{100})^{2}$

= $\dfrac{441}{440} ^{2}= (1 + \dfrac{r}{100})^{2}$

$square\: and\: square \:will \:cross\: with\: each \:other$

= $\dfrac{441}{440} = (1 + \dfrac{r}{100})$

= $\dfrac{441}{440} = (\dfrac{100 + r}{100})$

= $\dfrac{441}{440} × 100 = (100 + R)$

= $100.23 = 100 + r$

= $100.23 - 100 = r$

=$r = 0.23$%

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Answer 2

Given :-

• Principal = Rs.40000
• Amount = Rs.48620.25
• Time = 2 years.
• Rate = compounded half yearly .

To Find :-

• The rate of interest per annum. ?

Solution :-

we know that, when interest is compounded half yearly ,

• Rate becomes half .
• Time becomes double.

so,

• Time = 2 * 2 = 4 years.
• Rate = Let half yearly is R% .

then,

→ P[1 + (R/100)]^T = A

→ 40000[1 + (R/100)]⁴ = 48620.25

→ [1 + (R/100)]⁴ = 48620.25/40000

→ [1 + (R/100)]⁴ = (194481/160000)

→ [1 + (R/100)]⁴ = (21/20)⁴

→ 1 + (R/100) = (21/20)

→ (R/100) = (21/20) - 1

→ (R/100) = (21 - 20)/20

→ (R/100) = (1/20)

→ R = 5% .

therefore,

→ The rate of interest per annum = 5 * 2 = 10% (Ans.)

Learn more :-

CI in 2yr is Rs. 1600 and in 3 yrs it will be Rs. 1700. Find the rate of interest.

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