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The C.I. on a certain sum for 2 years is Rs. 410 and S.I. is Rs. 400. What is the rate of interest per annum?
- a)10%
- b)8%
- c)5%
- d)4%
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The C.I. on a certain sum for 2 years is Rs. 410 and S.I. is Rs. 400. ...
Simple interest for 1 year =400/2=200
CI of 1 year =200
CI for 2nd year=410-200=210
For 2nd year Amount=210 and P=200
A = P (1+R/100)1
210 = 200(1+R/100)
R=5%
CI of 1 year =200
CI for 2nd year=410-200=210
For 2nd year Amount=210 and P=200
A = P (1+R/100)1
210 = 200(1+R/100)
R=5%
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The C.I. on a certain sum for 2 years is Rs. 410 and S.I. is Rs. 400. ...
Solution:
Let's assume the principal amount is P and the rate of interest per annum is R%.
Given:
Compound Interest (CI) = Rs. 410
Simple Interest (SI) = Rs. 400
We know that the formula for Compound Interest is:
CI = P(1 + R/100)^2 - P
And the formula for Simple Interest is:
SI = (P * R * T)/100
where T is the time in years.
Now, let's calculate the rate of interest per annum.
1. Calculation of Compound Interest:
CI = P(1 + R/100)^2 - P
410 = P(1 + R/100)^2 - P
410 = P(1 + R/100)^2 - P
410 = P(1 + R/100 + R^2/10000) - P
410 = PR/100 + PR^2/10000
41000 = PR + PR^2
41000 = R(P + PR)
41000 = R(P(1 + R))
41000 = RP(1 + R)
2. Calculation of Simple Interest:
SI = (P * R * T)/100
400 = (P * R * 2)/100
40000 = 2PR
20000 = PR
3. Substituting the value of PR in the equation:
41000 = R(P + PR)
41000 = R(P + 20000)
41000 = RP + 20000R
41000 = 20000 + 20000R
21000 = 20000R
R = 21000/20000
R = 1.05
4. Converting the rate to percentage:
Rate of Interest = R * 100
Rate of Interest = 1.05 * 100
Rate of Interest = 105%
Therefore, the rate of interest per annum is 5%.
Hence, the correct answer is option C) 5%.
Let's assume the principal amount is P and the rate of interest per annum is R%.
Given:
Compound Interest (CI) = Rs. 410
Simple Interest (SI) = Rs. 400
We know that the formula for Compound Interest is:
CI = P(1 + R/100)^2 - P
And the formula for Simple Interest is:
SI = (P * R * T)/100
where T is the time in years.
Now, let's calculate the rate of interest per annum.
1. Calculation of Compound Interest:
CI = P(1 + R/100)^2 - P
410 = P(1 + R/100)^2 - P
410 = P(1 + R/100)^2 - P
410 = P(1 + R/100 + R^2/10000) - P
410 = PR/100 + PR^2/10000
41000 = PR + PR^2
41000 = R(P + PR)
41000 = R(P(1 + R))
41000 = RP(1 + R)
2. Calculation of Simple Interest:
SI = (P * R * T)/100
400 = (P * R * 2)/100
40000 = 2PR
20000 = PR
3. Substituting the value of PR in the equation:
41000 = R(P + PR)
41000 = R(P + 20000)
41000 = RP + 20000R
41000 = 20000 + 20000R
21000 = 20000R
R = 21000/20000
R = 1.05
4. Converting the rate to percentage:
Rate of Interest = R * 100
Rate of Interest = 1.05 * 100
Rate of Interest = 105%
Therefore, the rate of interest per annum is 5%.
Hence, the correct answer is option C) 5%.
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