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The simple and compound interest on a certain sum for two years are 4320 and 4579.2 find the sum and rate of interest?
Verified Answer
The simple and compound interest on a certain sum for two years are 43...
let P be the sum of money, r be the rate of interest (in decimal form), and t be the time in years.
The formula for simple interest is:
I = P * r * t
The formula for compound interest is:
A = P * (1 + r)^t
In this case, the simple interest on the sum for two years is 4320, and the compound interest on the sum for two years is 4579.2.
We can set up the following system of equations to represent these conditions:
I = P * r * 2
A = P * (1 + r)^2
Substituting the second equation into the first equation, we get:
I = P * r * 2
= P * (1 + r)^2 * r
= P * (1 + 2r + r^2)
Expanding the right-hand side, we get:
I = P + 2Pr + Pr^2
Substituting the given values for I and A, we get:
4320 = P + 2Pr + Pr^2
4579.2 = P * (1 + r)^2
Solving this system of equations, we get:
P = 3200
r = 0.06
Therefore, the sum of money is 3200, and the rate of interest is 6%.
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
The simple and compound interest on a certain sum for two years are 43...
Solution:
Let the Principal be P and Rate of Interest be R.
Then, Simple Interest for two years is (P * R * 2) / 100 = 0.02PR
Compound Interest for two years is P(1 + R/100)^2 - P = P(1 + 2R/100 + R^2/10000) - P = P(2R/100 + R^2/10000)
Given that, 0.02PR = 4579.2 - 4320 = 259.2
=> PR = 12,960
=> P = 12,960/R
Also, 0.02PR = P(2R/100 + R^2/10000) - P
=> 0.02R = 2R/100 + R^2/10000
=> 2R^2 - 98R - 2000 = 0
=> R = (98 ± sqrt(98^2 + 4 * 2 * 2000)) / 4 = 10 or 18.367
Therefore, the Principal is P = 12,960/10 = 1296 or P = 12,960/18.367 = 705.6
Since the Principal cannot be less than the Simple Interest, we can consider the Principal to be 1296 and the Rate of Interest to be 10%.
Hence, the sum is 1296 and the rate of interest is 10%.
Let the Principal be P and Rate of Interest be R.
Then, Simple Interest for two years is (P * R * 2) / 100 = 0.02PR
Compound Interest for two years is P(1 + R/100)^2 - P = P(1 + 2R/100 + R^2/10000) - P = P(2R/100 + R^2/10000)
Given that, 0.02PR = 4579.2 - 4320 = 259.2
=> PR = 12,960
=> P = 12,960/R
Also, 0.02PR = P(2R/100 + R^2/10000) - P
=> 0.02R = 2R/100 + R^2/10000
=> 2R^2 - 98R - 2000 = 0
=> R = (98 ± sqrt(98^2 + 4 * 2 * 2000)) / 4 = 10 or 18.367
Therefore, the Principal is P = 12,960/10 = 1296 or P = 12,960/18.367 = 705.6
Since the Principal cannot be less than the Simple Interest, we can consider the Principal to be 1296 and the Rate of Interest to be 10%.
Hence, the sum is 1296 and the rate of interest is 10%.
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The simple and compound interest on a certain sum for two years are 4320 and 4579.2 find the sum and rate of interest?
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The simple and compound interest on a certain sum for two years are 4320 and 4579.2 find the sum and rate of interest? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The simple and compound interest on a certain sum for two years are 4320 and 4579.2 find the sum and rate of interest? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The simple and compound interest on a certain sum for two years are 4320 and 4579.2 find the sum and rate of interest?.
The simple and compound interest on a certain sum for two years are 4320 and 4579.2 find the sum and rate of interest? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The simple and compound interest on a certain sum for two years are 4320 and 4579.2 find the sum and rate of interest? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The simple and compound interest on a certain sum for two years are 4320 and 4579.2 find the sum and rate of interest?.
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