At what rate percent will sum of Rs 4000 amount to Rs 4410 in 2 years compounded annually?

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

Let the rate percent be R.
We know that: 
\[CI = P \left( 1 + \frac{R}{100} \right)^n - P\]
\[410 = 4, 000 \left( 1 + \frac{R}{100} \right)^2 - 4, 000\]
\[4, 410 = 4, 000 \left( 1 + \frac{R}{100} \right)^2 \]
\[ \left( 1 + \frac{R}{100} \right)^2 = \frac{4, 410}{4, 000}\]
\[ \left( 1 + \frac{R}{100} \right)^2 = 1 . 1025\]
\[ \left( 1 + \frac{R}{100} \right)^2 = \left( 1 . 05 \right)^2 \]
\[1 + \frac{R}{100} = 1 . 05\]
\[\frac{R}{100} = 0 . 05\]
R = 5
Thus, the required rate percent is 5.

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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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