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The difference between the compound interest, compounded annually and the simple interest on a certain sum for 2 years at 6% per annum is $ 18. Find the sum.
- a)$ 8110
- b)$ 4300
- c)$ 5000
- d)$ 5290
Correct answer is option 'C'. Can you explain this answer?
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The difference between the compound interest, compounded annually and...
Difference between Compound Interest and Simple Interest
To find the sum, we need to understand the difference between compound interest and simple interest.
- Simple Interest (SI): Simple interest is calculated on the original principal amount only. It does not take into account any interest earned in previous periods.
- Compound Interest (CI): Compound interest is calculated on both the original principal amount and any interest earned in previous periods. It is more advantageous as it allows the interest to accumulate over time.
Given Information
- Time period: 2 years
- Rate of interest: 6% per annum
- Difference between CI and SI: $18
Formula
The formula to calculate compound interest is:
CI = P(1 + r/n)^(nt) - P
Where:
- P is the principal sum
- r is the rate of interest
- n is the number of times the interest is compounded per year
- t is the number of years
The formula to calculate simple interest is:
SI = P * r * t
Solution
Let the principal sum be P.
We know that the difference between CI and SI is $18.
So, CI - SI = $18
Using the formulas, we can calculate the CI and SI.
CI = P(1 + r/100)^2 - P
SI = P * r * t
Substituting the values, we get:
P(1 + 6/100)^2 - P - P * 6 * 2 = $18
Simplifying the equation:
P(1.06^2 - 1 - 0.12) = $18
P(1.1236 - 1 - 0.12) = $18
P(0.0036) = $18
P = $18 / 0.0036
P = $5000
Therefore, the sum is $5000.
Hence, the correct answer is option C) $5000.
To find the sum, we need to understand the difference between compound interest and simple interest.
- Simple Interest (SI): Simple interest is calculated on the original principal amount only. It does not take into account any interest earned in previous periods.
- Compound Interest (CI): Compound interest is calculated on both the original principal amount and any interest earned in previous periods. It is more advantageous as it allows the interest to accumulate over time.
Given Information
- Time period: 2 years
- Rate of interest: 6% per annum
- Difference between CI and SI: $18
Formula
The formula to calculate compound interest is:
CI = P(1 + r/n)^(nt) - P
Where:
- P is the principal sum
- r is the rate of interest
- n is the number of times the interest is compounded per year
- t is the number of years
The formula to calculate simple interest is:
SI = P * r * t
Solution
Let the principal sum be P.
We know that the difference between CI and SI is $18.
So, CI - SI = $18
Using the formulas, we can calculate the CI and SI.
CI = P(1 + r/100)^2 - P
SI = P * r * t
Substituting the values, we get:
P(1 + 6/100)^2 - P - P * 6 * 2 = $18
Simplifying the equation:
P(1.06^2 - 1 - 0.12) = $18
P(1.1236 - 1 - 0.12) = $18
P(0.0036) = $18
P = $18 / 0.0036
P = $5000
Therefore, the sum is $5000.
Hence, the correct answer is option C) $5000.
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The difference between the compound interest, compounded annually and the simple interest on a certain sum for 2 years at 6% per annum is $ 18. Find the sum.a)$ 8110b)$ 4300c)$ 5000d)$ 5290Correct answer is option 'C'. Can you explain this answer?
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