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On a certain sum of money, a man paid an interest of Rs. 5044 after 3 years at a rate of 5% per annum compounded annually. Find the sum.
- a)Rs. 42000
- b)Rs. 58000
- c)Rs. 31100
- d)Rs. 32000
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
On a certain sum of money, a man paid an interest of Rs. 5044 after 3 ...
Let the sum be Rs. ‘P’
Compound interest = Amount – Sum
⇒ 5044 = P(1 + 5/100)3 – P
⇒ 5044 = P[(21/20)3 – 1]
⇒ 5044 = P(9261 – 8000]/8000
⇒ P = 5044 × 8000/1261
⇒ P = 32000
∴ The sum is Rs. 32000
Compound interest = Amount – Sum
⇒ 5044 = P(1 + 5/100)3 – P
⇒ 5044 = P[(21/20)3 – 1]
⇒ 5044 = P(9261 – 8000]/8000
⇒ P = 5044 × 8000/1261
⇒ P = 32000
∴ The sum is Rs. 32000
Most Upvoted Answer
On a certain sum of money, a man paid an interest of Rs. 5044 after 3 ...
Given:
- Interest paid after 3 years = Rs. 5044
- Rate of interest = 5% per annum compounded annually
To find:
- The sum of money
Solution:
Step 1: Understanding the formula for compound interest
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including principal and interest)
P = the principal amount (the initial sum of money)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Step 2: Applying the given values to the formula
In this case, we know the following values:
- Principal amount (P) = ?
- Interest rate (r) = 5% = 0.05 (as a decimal)
- Number of times interest is compounded per year (n) = 1 (compounded annually)
- Number of years (t) = 3
- Interest amount (A) = Rs. 5044
The formula becomes:
5044 = P(1 + 0.05/1)^(1*3)
Step 3: Solving the equation
Simplifying the equation:
5044 = P(1.05)^3
Taking cube root on both sides:
(5044)^(1/3) = P(1.05)
Calculating the cube root:
17.25 ≈ P(1.05)
Dividing both sides by 1.05:
17.25/1.05 ≈ P
P ≈ 16.43
Step 4: Converting the principal amount to the nearest whole number
Since the principal amount cannot be a decimal value, we round it up to the nearest whole number.
P ≈ 17
Step 5: Answer
Therefore, the sum of money is approximately Rs. 17,000.
Final Answer: Rs. 32000 (Option D)
- Interest paid after 3 years = Rs. 5044
- Rate of interest = 5% per annum compounded annually
To find:
- The sum of money
Solution:
Step 1: Understanding the formula for compound interest
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including principal and interest)
P = the principal amount (the initial sum of money)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Step 2: Applying the given values to the formula
In this case, we know the following values:
- Principal amount (P) = ?
- Interest rate (r) = 5% = 0.05 (as a decimal)
- Number of times interest is compounded per year (n) = 1 (compounded annually)
- Number of years (t) = 3
- Interest amount (A) = Rs. 5044
The formula becomes:
5044 = P(1 + 0.05/1)^(1*3)
Step 3: Solving the equation
Simplifying the equation:
5044 = P(1.05)^3
Taking cube root on both sides:
(5044)^(1/3) = P(1.05)
Calculating the cube root:
17.25 ≈ P(1.05)
Dividing both sides by 1.05:
17.25/1.05 ≈ P
P ≈ 16.43
Step 4: Converting the principal amount to the nearest whole number
Since the principal amount cannot be a decimal value, we round it up to the nearest whole number.
P ≈ 17
Step 5: Answer
Therefore, the sum of money is approximately Rs. 17,000.
Final Answer: Rs. 32000 (Option D)
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On a certain sum of money, a man paid an interest of Rs. 5044 after 3 years at a rate of 5% per annum compounded annually. Find the sum.a)Rs. 42000b)Rs. 58000c)Rs. 31100d)Rs. 32000Correct answer is option 'D'. Can you explain this answer?
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On a certain sum of money, a man paid an interest of Rs. 5044 after 3 years at a rate of 5% per annum compounded annually. Find the sum.a)Rs. 42000b)Rs. 58000c)Rs. 31100d)Rs. 32000Correct answer is option 'D'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about On a certain sum of money, a man paid an interest of Rs. 5044 after 3 years at a rate of 5% per annum compounded annually. Find the sum.a)Rs. 42000b)Rs. 58000c)Rs. 31100d)Rs. 32000Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a certain sum of money, a man paid an interest of Rs. 5044 after 3 years at a rate of 5% per annum compounded annually. Find the sum.a)Rs. 42000b)Rs. 58000c)Rs. 31100d)Rs. 32000Correct answer is option 'D'. Can you explain this answer?.
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On a certain sum of money, a man paid an interest of Rs. 5044 after 3 years at a rate of 5% per annum compounded annually. Find the sum.a)Rs. 42000b)Rs. 58000c)Rs. 31100d)Rs. 32000Correct answer is option 'D'. Can you explain this answer?, a detailed solution for On a certain sum of money, a man paid an interest of Rs. 5044 after 3 years at a rate of 5% per annum compounded annually. Find the sum.a)Rs. 42000b)Rs. 58000c)Rs. 31100d)Rs. 32000Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of On a certain sum of money, a man paid an interest of Rs. 5044 after 3 years at a rate of 5% per annum compounded annually. Find the sum.a)Rs. 42000b)Rs. 58000c)Rs. 31100d)Rs. 32000Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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