CAT Exam > CAT Questions > If the difference between simple interest and...
Start Learning for Free
If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be?
Most Upvoted Answer
If the difference between simple interest and compound interest on som...
Understanding the problem:
We are given that the difference between simple interest and compound interest on a principal amount at 20% per annum for three years is 48. We need to find the principal amount.
Key Formula:
The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = The final amount
P = The principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Number of years
Step-by-step solution:
Step 1: Let's assume the principal amount is P.
Step 2: Calculate the compound interest using the given formula:
A = P(1 + r/n)^(nt)
A = P(1 + 0.20/1)^(1 * 3)
A = P(1 + 0.20)^3
A = P(1.20)^3
The compound interest is given by the difference between the final amount and the principal amount:
Compound Interest = A - P
Step 3: Calculate the simple interest for the same principal amount, rate, and time:
Simple Interest = P * r * t
Simple Interest = P * 0.20 * 3
Step 4: The difference between the simple interest and compound interest is given as 48:
Compound Interest - Simple Interest = 48
Step 5: Substitute the values and solve the equation:
P(1.20)^3 - P * 0.20 * 3 = 48
P(1.728) - P * 0.60 = 48
Simplifying further:
1.728P - 0.60P = 48
1.128P = 48
P = 48 / 1.128
P = 42.55 (Approximately)
Therefore, the principal amount is approximately 42.55.
We are given that the difference between simple interest and compound interest on a principal amount at 20% per annum for three years is 48. We need to find the principal amount.
Key Formula:
The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = The final amount
P = The principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Number of years
Step-by-step solution:
Step 1: Let's assume the principal amount is P.
Step 2: Calculate the compound interest using the given formula:
A = P(1 + r/n)^(nt)
A = P(1 + 0.20/1)^(1 * 3)
A = P(1 + 0.20)^3
A = P(1.20)^3
The compound interest is given by the difference between the final amount and the principal amount:
Compound Interest = A - P
Step 3: Calculate the simple interest for the same principal amount, rate, and time:
Simple Interest = P * r * t
Simple Interest = P * 0.20 * 3
Step 4: The difference between the simple interest and compound interest is given as 48:
Compound Interest - Simple Interest = 48
Step 5: Substitute the values and solve the equation:
P(1.20)^3 - P * 0.20 * 3 = 48
P(1.728) - P * 0.60 = 48
Simplifying further:
1.728P - 0.60P = 48
1.128P = 48
P = 48 / 1.128
P = 42.55 (Approximately)
Therefore, the principal amount is approximately 42.55.
Community Answer
If the difference between simple interest and compound interest on som...
Principal is 375
try to find on 100 and equate the amount
the difference of ci and si on 100 rs ( 4*3) + 0.8 ( 4*20%)
so 12.8 rs
now 12.8 on 100 then 48 rs on x
cross multiply you will get 375
try to find on 100 and equate the amount
the difference of ci and si on 100 rs ( 4*3) + 0.8 ( 4*20%)
so 12.8 rs
now 12.8 on 100 then 48 rs on x
cross multiply you will get 375
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be?
Question Description
If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be?.
If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be?.
Solutions for If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? defined & explained in the simplest way possible. Besides giving the explanation of
If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be?, a detailed solution for If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? has been provided alongside types of If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? theory, EduRev gives you an
ample number of questions to practice If the difference between simple interest and compound interest on some principal amount at 20% per annum for three years is 48. Then the principle must be? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup