At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years when compounded annually?

• Anshusonalika
• 4 years ago
• Matematika

At what rate percent per annum will₹4000 amount to₹4410 in2 years when compounded annually?

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• 1 जवाब

• Bhavyamishra
• 4 years ago
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Intrest =amount-principle
=4410-4000
=410

SI=(p×r×t)÷100
410=(4000×r×2)÷100
410×100=8000×r
41000÷8000=r
5•125=r

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अतिथि के रूप में पोस्ट करें

Name

ईमेल

Here the amount A = 4410
principle is = 4000 and rate is 5% = 5/100 = 0.05 per annum... let n = time

so A = p(1+r)ⁿ
=> 4410 = 4000(1+0.05)ⁿ
=> (1.05)ⁿ = 441/400 = 1.1025
=> n = 2.

so, time is 2 years.

At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years

Question:

At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years when compounded annually?

Solution:

Let $R \% p . a .$ be the required rate.

$A=4410$

$P=4000$

$n=2$ years

Now,$A=\mathrm{P}\left(1+\frac{R}{100}\right)^{n}$

$\Rightarrow 4410=4000\left(1+\frac{\mathrm{R}}{100}\right)^{2}$

$\Rightarrow \frac{4410}{4000}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow \frac{441}{400}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow\left(\frac{21}{20}\right)^{2}=\left(1+\frac{R}{100}\right)^{2}$

$\Rightarrow \frac{21}{20}-1=\frac{R}{100}$

$\Rightarrow \frac{21-20}{20}=\frac{R}{100}$

$\Rightarrow \frac{1}{20}=\frac{R}{100}$

$\Rightarrow R=\left(\frac{1 \times 100}{20}\right)=5$

Hence, the required rate is $5 \%$ p.a.

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At what rate percent per annum will a sum of Rs. 4000 yield compound interest of Rs. 410 in 2 years?

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Solution

Principal (P) = Rs. 4000 C.I = Rs. 410 ∴ Amount (A) = Rs. 4000 + 410 = Rs. 4410 Let rate =R% p.a. Period (n) = 2 years. ∴ Amount =P(1+R100)n ⇒AP=(1+R100)2 ⇒Rs.44104000=(1+R100)n ⇒4414000=[1+R100]2 ⇒(2120)2=(1+R100)2 Comparing, we get 1+R100=2120=1+120 ∴R100=120⇒R=10020=5 ∴ Rate =5% p.a

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