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At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compound interest?
Most Upvoted Answer
At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compo...
Amount = principal ( 1 + r/100 ) ^t
2315.25 = 2000 ( 1 + r/100 ) ³
2315.25 / 2000 = ( 1 + r/100 ) ³
2315.25 × 4 / 2000 × 4 = ( 1 + r/100 ) ³
9261 / 8000 = ( 1 + r/100 ) ³
cube root both sides
³√9261 / ³√8000 = ³√ ( 1 + r/100 ) ³
21 / 20 = ( 1 + r/100 ) ³/³
21 / 20 = ( 1 + r/100 )
21 / 20 - 1 = r/100
21 / 20 - 20/20 = r/100
(1 / 20 ) 100 = r
5 = r
rate = 5%
2315.25 = 2000 ( 1 + r/100 ) ³
2315.25 / 2000 = ( 1 + r/100 ) ³
2315.25 × 4 / 2000 × 4 = ( 1 + r/100 ) ³
9261 / 8000 = ( 1 + r/100 ) ³
cube root both sides
³√9261 / ³√8000 = ³√ ( 1 + r/100 ) ³
21 / 20 = ( 1 + r/100 ) ³/³
21 / 20 = ( 1 + r/100 )
21 / 20 - 1 = r/100
21 / 20 - 20/20 = r/100
(1 / 20 ) 100 = r
5 = r
rate = 5%
Community Answer
At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compo...
Given:
Principal amount (P) = ₹2000
Amount (A) = ₹2315.25
Time (t) = 3 years
We need to find the rate percent at which ₹2000 will amount to ₹2315.25 in 3 years at compound interest.
Formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Amount
P = Principal amount
r = Rate of interest per period
n = Number of periods
t = Time in years
Step 1:
Let's assume the rate of interest per period as 'x' percent.
Step 2:
Substitute the given values in the formula:
2315.25 = 2000(1 + x/100)^(1*3)
Divide both sides by 2000 to simplify the equation:
1.157625 = (1 + x/100)^3
Step 3:
Take the cube root of both sides to isolate the (1 + x/100) term:
1 + x/100 = (1.157625)^(1/3)
1 + x/100 = 1.0425
Step 4:
Subtract 1 from both sides to isolate the x/100 term:
x/100 = 1.0425 - 1
x/100 = 0.0425
Step 5:
Multiply both sides by 100 to solve for x:
x = 0.0425 * 100
x = 4.25
Answer:
The rate percent at which ₹2000 will amount to ₹2315.25 in 3 years at compound interest is 4.25%.
Principal amount (P) = ₹2000
Amount (A) = ₹2315.25
Time (t) = 3 years
We need to find the rate percent at which ₹2000 will amount to ₹2315.25 in 3 years at compound interest.
Formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Amount
P = Principal amount
r = Rate of interest per period
n = Number of periods
t = Time in years
Step 1:
Let's assume the rate of interest per period as 'x' percent.
Step 2:
Substitute the given values in the formula:
2315.25 = 2000(1 + x/100)^(1*3)
Divide both sides by 2000 to simplify the equation:
1.157625 = (1 + x/100)^3
Step 3:
Take the cube root of both sides to isolate the (1 + x/100) term:
1 + x/100 = (1.157625)^(1/3)
1 + x/100 = 1.0425
Step 4:
Subtract 1 from both sides to isolate the x/100 term:
x/100 = 1.0425 - 1
x/100 = 0.0425
Step 5:
Multiply both sides by 100 to solve for x:
x = 0.0425 * 100
x = 4.25
Answer:
The rate percent at which ₹2000 will amount to ₹2315.25 in 3 years at compound interest is 4.25%.
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At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compound interest? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compound interest? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compound interest?.
At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compound interest? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compound interest? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what rate percent will ₹2000 amount to ₹2315.25 in 3 years at compound interest?.
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