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A sum of money, at compound interest, yields Rs. 200 and Rs. 220 at the end of first and second years respectively. What is the rate percent?
- a)20%
- b)15%
- c)10%
- d)5%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A sum of money, at compound interest, yields Rs. 200 and Rs. 220 at th...
Difference between interests = Rs.220 - Rs. 200 = Rs. 20
⇒ Rs. 20 is the S.I on Rs. 200 for 1 Year.
Hence, the rate of interest is 10%.
⇒ Rs. 20 is the S.I on Rs. 200 for 1 Year.
Hence, the rate of interest is 10%.
Most Upvoted Answer
A sum of money, at compound interest, yields Rs. 200 and Rs. 220 at th...
Given information:
- The sum of money yields Rs. 200 at the end of the first year.
- The sum of money yields Rs. 220 at the end of the second year.
To find:
- The rate percent.
Solution:
Let's assume that the principal amount (initial sum of money) is P and the rate of interest is R%.
Calculation of Compound Interest:
The compound interest for the first year is given by:
C.I. = P + P(R/100) = P(1 + R/100) = 200
The compound interest for the second year is given by:
C.I. = P(1 + R/100) + P(R/100) = P(1 + R/100)² = 220
Now, we can solve these two equations to find the value of R.
Simplifying the equations:
Equation 1: P(1 + R/100) = 200
Equation 2: P(1 + R/100)² = 220
Dividing Equation 2 by Equation 1:
(P(1 + R/100)²) / (P(1 + R/100)) = 220 / 200
Simplifying, we get:
1 + R/100 = 11/10
Subtracting 1 from both sides:
R/100 = 11/10 - 1
R/100 = 1/10
Multiplying both sides by 100:
R = 100/10 = 10
Therefore, the rate of interest is 10%.
Conclusion:
The correct answer is option 'c', i.e., 10%.
- The sum of money yields Rs. 200 at the end of the first year.
- The sum of money yields Rs. 220 at the end of the second year.
To find:
- The rate percent.
Solution:
Let's assume that the principal amount (initial sum of money) is P and the rate of interest is R%.
Calculation of Compound Interest:
The compound interest for the first year is given by:
C.I. = P + P(R/100) = P(1 + R/100) = 200
The compound interest for the second year is given by:
C.I. = P(1 + R/100) + P(R/100) = P(1 + R/100)² = 220
Now, we can solve these two equations to find the value of R.
Simplifying the equations:
Equation 1: P(1 + R/100) = 200
Equation 2: P(1 + R/100)² = 220
Dividing Equation 2 by Equation 1:
(P(1 + R/100)²) / (P(1 + R/100)) = 220 / 200
Simplifying, we get:
1 + R/100 = 11/10
Subtracting 1 from both sides:
R/100 = 11/10 - 1
R/100 = 1/10
Multiplying both sides by 100:
R = 100/10 = 10
Therefore, the rate of interest is 10%.
Conclusion:
The correct answer is option 'c', i.e., 10%.
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A sum of money, at compound interest, yields Rs. 200 and Rs. 220 at the end of first and second years respectively. What is the rate percent?a)20%b)15%c)10%d)5%Correct answer is option 'C'. Can you explain this answer?
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