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The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum is:
- a)Rs.600
- b)Rs.645
- c)Rs.525
- d)Rs.625
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The difference between simple and compound interests compounded annual...
sum = Rs.x
C.I = [x(1+4/100)^2-x] = (676/625x-x) = 51/625
S.I = (x*4*2)/100 = 2x/25
x = 625
Most Upvoted Answer
The difference between simple and compound interests compounded annual...
Given:
- Time period (n) = 2 years
- Rate of interest (r) = 4% per annum
- Difference between compound interest and simple interest = Re. 1
To Find:
The principal sum (P)
Formula:
1. Simple Interest (SI) = P * r * n / 100
2. Compound Interest (CI) = P * (1 + r/100)^n - P
Calculation:
Let's assume the principal sum is P.
Step 1: Calculate Simple Interest (SI):
SI = P * r * n / 100
Step 2: Calculate Compound Interest (CI):
CI = P * (1 + r/100)^n - P
Step 3: Calculate the Difference between CI and SI:
Difference = CI - SI
Re. 1 = P * (1 + r/100)^n - P - P * r * n / 100
Step 4: Substitute the given values:
Re. 1 = P * (1 + 4/100)^2 - P - P * 4 * 2 / 100
Re. 1 = P * (1 + 0.04)^2 - P - P * 0.08
Step 5: Simplify the equation:
Re. 1 = P * (1.04)^2 - P - 0.08P
Re. 1 = P * 1.0816 - P - 0.08P
Re. 1 = 1.0816P - P - 0.08P
Re. 1 = 0.0016P
Step 6: Solve for P:
Re. 1 = 0.0016P
P = Re. 1 / 0.0016
P = Rs. 625
Therefore, the principal sum is Rs. 625. Hence, the correct answer is option D.
- Time period (n) = 2 years
- Rate of interest (r) = 4% per annum
- Difference between compound interest and simple interest = Re. 1
To Find:
The principal sum (P)
Formula:
1. Simple Interest (SI) = P * r * n / 100
2. Compound Interest (CI) = P * (1 + r/100)^n - P
Calculation:
Let's assume the principal sum is P.
Step 1: Calculate Simple Interest (SI):
SI = P * r * n / 100
Step 2: Calculate Compound Interest (CI):
CI = P * (1 + r/100)^n - P
Step 3: Calculate the Difference between CI and SI:
Difference = CI - SI
Re. 1 = P * (1 + r/100)^n - P - P * r * n / 100
Step 4: Substitute the given values:
Re. 1 = P * (1 + 4/100)^2 - P - P * 4 * 2 / 100
Re. 1 = P * (1 + 0.04)^2 - P - P * 0.08
Step 5: Simplify the equation:
Re. 1 = P * (1.04)^2 - P - 0.08P
Re. 1 = P * 1.0816 - P - 0.08P
Re. 1 = 1.0816P - P - 0.08P
Re. 1 = 0.0016P
Step 6: Solve for P:
Re. 1 = 0.0016P
P = Re. 1 / 0.0016
P = Rs. 625
Therefore, the principal sum is Rs. 625. Hence, the correct answer is option D.
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The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum is:a)Rs.600b)Rs.645c)Rs.525d)Rs.625Correct answer is option 'D'. Can you explain this answer?
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