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The difference between compound interest and simple interest on an amount of Rs 15,000 for 2 years is Rs 96. What is the rate of interest per annum?
- a)8
- b)10
- c)9
- d)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The difference between compound interest and simple interest on an amo...
[15000 (1+ r/100)2 – 15000] – (15000 × r × 2)/100 = 96
By solving the above equation
r2 = (96 × 2)/3 = 64
Therefore r = 8%
By solving the above equation
r2 = (96 × 2)/3 = 64
Therefore r = 8%
Most Upvoted Answer
The difference between compound interest and simple interest on an amo...
Simple Interest Formula:
Simple Interest (SI) = (Principal x Rate x Time) / 100
Compound Interest Formula:
Compound Interest (CI) = Principal x [(1 + Rate/100)^(Time)] - Principal
Given:
Principal (P) = Rs 15,000
Time (T) = 2 years
Difference between CI and SI = Rs 96
To find:
Rate of Interest per annum
Let's calculate the Simple Interest and Compound Interest first.
Simple Interest (SI):
SI = (P x R x T) / 100
SI = (15000 x R x 2) / 100
SI = 300R
Compound Interest (CI):
CI = P x [(1 + R/100)^(T)] - P
CI = 15000 x [(1 + R/100)^(2)] - 15000
CI = 15000 x (1 + 2R/100 + (R/100)^2) - 15000
CI = 15000 + 300R + 15R^2 - 15000
CI = 300R + 15R^2
Given that the difference between CI and SI is Rs 96:
CI - SI = 96
(300R + 15R^2) - 300R = 96
15R^2 = 96
R^2 = 96/15
R^2 = 6.4
Taking the square root of both sides:
R = √6.4
R ≈ 2.53
The rate of interest per annum is approximately 2.53%.
Now, let's check the options given:
a) 8% - Not the correct answer
b) 10% - Not the correct answer
c) 9% - Not the correct answer
d) Cannot be determined - Not the correct answer
Therefore, the correct answer is option 'A' - 2.53%.
Simple Interest (SI) = (Principal x Rate x Time) / 100
Compound Interest Formula:
Compound Interest (CI) = Principal x [(1 + Rate/100)^(Time)] - Principal
Given:
Principal (P) = Rs 15,000
Time (T) = 2 years
Difference between CI and SI = Rs 96
To find:
Rate of Interest per annum
Let's calculate the Simple Interest and Compound Interest first.
Simple Interest (SI):
SI = (P x R x T) / 100
SI = (15000 x R x 2) / 100
SI = 300R
Compound Interest (CI):
CI = P x [(1 + R/100)^(T)] - P
CI = 15000 x [(1 + R/100)^(2)] - 15000
CI = 15000 x (1 + 2R/100 + (R/100)^2) - 15000
CI = 15000 + 300R + 15R^2 - 15000
CI = 300R + 15R^2
Given that the difference between CI and SI is Rs 96:
CI - SI = 96
(300R + 15R^2) - 300R = 96
15R^2 = 96
R^2 = 96/15
R^2 = 6.4
Taking the square root of both sides:
R = √6.4
R ≈ 2.53
The rate of interest per annum is approximately 2.53%.
Now, let's check the options given:
a) 8% - Not the correct answer
b) 10% - Not the correct answer
c) 9% - Not the correct answer
d) Cannot be determined - Not the correct answer
Therefore, the correct answer is option 'A' - 2.53%.
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The difference between compound interest and simple interest on an amount of Rs 15,000 for 2 years is Rs96. What is the rate of interest per annum?a)8b)10c)9d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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