- 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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- Bhavyamishra
- 4 years ago
- Report
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
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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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