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The simple interest accrued on a sum of certain principal is Rs. 7,200 in six years at the rate of 12 p.c.p.a. What would be the compound interest accrued on that principal at the rate of 5 p.c.p.a. in 2 years?
- a)Rs. 1,020
- b)Rs. 1,055
- c)Rs. 2,050
- d)Rs. 1,025
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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The simple interest accrued on a sum of certain principal is Rs. 7,200...
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The simple interest accrued on a sum of certain principal is Rs. 7,200...
To calculate the compound interest accrued on a principal amount, we use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including both principal and interest)
P = principal amount
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given information:
Principal amount (P) = unknown
Simple interest accrued in 6 years = Rs. 7,200
Rate of interest (r) = 12% per annum
Compound interest rate (r) = 5% per annum
Time (t) = 2 years
Step 1: Calculating the principal amount using simple interest formula
The simple interest formula is given by:
Simple Interest (SI) = (P * r * t) / 100
Substituting the given values:
7,200 = (P * 12 * 6) / 100
Simplifying the equation:
7,200 = (P * 72) / 100
7,200 * 100 = P * 72
720,000 = 72P
P = 720,000 / 72
P = Rs. 10,000
Therefore, the principal amount is Rs. 10,000.
Step 2: Calculating the compound interest
Using the compound interest formula:
A = P(1 + r/n)^(nt)
Substituting the given values:
A = 10,000(1 + 0.05/1)^(1*2)
Simplifying the equation:
A = 10,000(1 + 0.05)^2
A = 10,000(1.05)^2
A = 10,000(1.1025)
A = Rs. 11,025
The compound interest accrued on the principal amount at the rate of 5% per annum for 2 years is Rs. 11,025 - Rs. 10,000 = Rs. 1,025.
Therefore, the correct answer is option D) Rs. 1,025.
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including both principal and interest)
P = principal amount
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given information:
Principal amount (P) = unknown
Simple interest accrued in 6 years = Rs. 7,200
Rate of interest (r) = 12% per annum
Compound interest rate (r) = 5% per annum
Time (t) = 2 years
Step 1: Calculating the principal amount using simple interest formula
The simple interest formula is given by:
Simple Interest (SI) = (P * r * t) / 100
Substituting the given values:
7,200 = (P * 12 * 6) / 100
Simplifying the equation:
7,200 = (P * 72) / 100
7,200 * 100 = P * 72
720,000 = 72P
P = 720,000 / 72
P = Rs. 10,000
Therefore, the principal amount is Rs. 10,000.
Step 2: Calculating the compound interest
Using the compound interest formula:
A = P(1 + r/n)^(nt)
Substituting the given values:
A = 10,000(1 + 0.05/1)^(1*2)
Simplifying the equation:
A = 10,000(1 + 0.05)^2
A = 10,000(1.05)^2
A = 10,000(1.1025)
A = Rs. 11,025
The compound interest accrued on the principal amount at the rate of 5% per annum for 2 years is Rs. 11,025 - Rs. 10,000 = Rs. 1,025.
Therefore, the correct answer is option D) Rs. 1,025.
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The simple interest accrued on a sum of certain principal is Rs. 7,200 in six years at the rate of 12 p.c.p.a. What would be the compound interest accrued on that principal at the rate of 5 p.c.p.a. in 2 years?a)Rs. 1,020b)Rs. 1,055c)Rs. 2,050d)Rs. 1,025e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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