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At what rate percent per annum the compound interest on Rs. 12000 amounted to Rs. 14700 in 3 years.?
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At what rate percent per annum the compound interest on Rs. 12000 amou...
Understanding the Problem
To determine the rate of compound interest, we need to find the interest rate that makes an initial investment of Rs. 12,000 grow to Rs. 14,700 in 3 years.
Given Data
- Principal (P): Rs. 12,000
- Amount (A): Rs. 14,700
- Time (T): 3 years
Formula for Compound Interest
The formula for the amount in compound interest is:
A = P(1 + r/n)^(nt)
Where:
- A = final amount
- P = principal amount
- r = annual interest rate (as a decimal)
- n = number of times interest applied per time period
- t = time the money is invested for in years
For this problem, we will assume interest is compounded annually (n=1).
Calculation Steps
1. Substituting the Values
We need to rearrange the formula to find the rate (r):
14,700 = 12,000(1 + r)^3
2. Dividing Both Sides by Principal
(1 + r)^3 = 14,700 / 12,000
(1 + r)^3 = 1.225
3. Finding the Cube Root
1 + r = (1.225)^(1/3)
1 + r ≈ 1.075
4. Solving for r
r ≈ 1.075 - 1
r ≈ 0.075
5. Converting to Percentage
Rate (r) = 0.075 × 100 ≈ 7.5%
Final Result
The compound interest rate is approximately 7.5% per annum.
To determine the rate of compound interest, we need to find the interest rate that makes an initial investment of Rs. 12,000 grow to Rs. 14,700 in 3 years.
Given Data
- Principal (P): Rs. 12,000
- Amount (A): Rs. 14,700
- Time (T): 3 years
Formula for Compound Interest
The formula for the amount in compound interest is:
A = P(1 + r/n)^(nt)
Where:
- A = final amount
- P = principal amount
- r = annual interest rate (as a decimal)
- n = number of times interest applied per time period
- t = time the money is invested for in years
For this problem, we will assume interest is compounded annually (n=1).
Calculation Steps
1. Substituting the Values
We need to rearrange the formula to find the rate (r):
14,700 = 12,000(1 + r)^3
2. Dividing Both Sides by Principal
(1 + r)^3 = 14,700 / 12,000
(1 + r)^3 = 1.225
3. Finding the Cube Root
1 + r = (1.225)^(1/3)
1 + r ≈ 1.075
4. Solving for r
r ≈ 1.075 - 1
r ≈ 0.075
5. Converting to Percentage
Rate (r) = 0.075 × 100 ≈ 7.5%
Final Result
The compound interest rate is approximately 7.5% per annum.
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At what rate percent per annum the compound interest on Rs. 12000 amounted to Rs. 14700 in 3 years.?
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At what rate percent per annum the compound interest on Rs. 12000 amounted to Rs. 14700 in 3 years.? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about At what rate percent per annum the compound interest on Rs. 12000 amounted to Rs. 14700 in 3 years.? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what rate percent per annum the compound interest on Rs. 12000 amounted to Rs. 14700 in 3 years.?.
At what rate percent per annum the compound interest on Rs. 12000 amounted to Rs. 14700 in 3 years.? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about At what rate percent per annum the compound interest on Rs. 12000 amounted to Rs. 14700 in 3 years.? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what rate percent per annum the compound interest on Rs. 12000 amounted to Rs. 14700 in 3 years.?.
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