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If the difference between the CI and SI on a sum of money at 5% per annum for 2years is Rs.16.Find the Simple Interest ?
- a)180
- b)460
- c)520
- d)640
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If the difference between the CI and SI on a sum of money at 5% per an...
16 =P*(5/100)2
P = 6400
SI =(6400*5*2)/100 =640
P = 6400
SI =(6400*5*2)/100 =640
Most Upvoted Answer
If the difference between the CI and SI on a sum of money at 5% per an...
To solve this question, we need to understand the concepts of Compound Interest (CI) and Simple Interest (SI).
CI is the interest calculated on both the initial principal and the accumulated interest from previous periods. It is calculated using the formula:
CI = P(1 + r/n)^(nt) - P
where P is the principal amount, r is the rate of interest, n is the number of times the interest is compounded per year, and t is the number of years.
On the other hand, SI is the interest calculated only on the principal amount for a given period of time. It is calculated using the formula:
SI = P * r * t
where P is the principal amount, r is the rate of interest, and t is the number of years.
In this question, we are given that the difference between CI and SI for a sum of money is Rs. 16 at an interest rate of 5% per annum for 2 years.
Let's assume the principal amount is P.
The difference between CI and SI can be calculated as:
CI - SI = 16
Using the formulas mentioned above, we can substitute the values and solve for P.
P(1 + 0.05/n)^(n*2) - P - P * 0.05 * 2 = 16
Simplifying the equation further, we get:
P[(1 + 0.05/n)^(2n) - 1 - 0.1] = 16
Now, let's consider different options to find the correct value of P.
Option (a): 180
If we substitute P = 180 in the equation, we can see that the left-hand side of the equation does not equal 16.
Option (b): 460
If we substitute P = 460 in the equation, we can see that the left-hand side of the equation does not equal 16.
Option (c): 520
If we substitute P = 520 in the equation, we can see that the left-hand side of the equation does not equal 16.
Option (d): 640
If we substitute P = 640 in the equation, we can see that the left-hand side of the equation equals 16.
Therefore, the correct option is (d) 640.
Hence, the Simple Interest is Rs. 640.
Note: It is important to verify the answer by substituting the value of P in the original equation to ensure it satisfies the given conditions.
CI is the interest calculated on both the initial principal and the accumulated interest from previous periods. It is calculated using the formula:
CI = P(1 + r/n)^(nt) - P
where P is the principal amount, r is the rate of interest, n is the number of times the interest is compounded per year, and t is the number of years.
On the other hand, SI is the interest calculated only on the principal amount for a given period of time. It is calculated using the formula:
SI = P * r * t
where P is the principal amount, r is the rate of interest, and t is the number of years.
In this question, we are given that the difference between CI and SI for a sum of money is Rs. 16 at an interest rate of 5% per annum for 2 years.
Let's assume the principal amount is P.
The difference between CI and SI can be calculated as:
CI - SI = 16
Using the formulas mentioned above, we can substitute the values and solve for P.
P(1 + 0.05/n)^(n*2) - P - P * 0.05 * 2 = 16
Simplifying the equation further, we get:
P[(1 + 0.05/n)^(2n) - 1 - 0.1] = 16
Now, let's consider different options to find the correct value of P.
Option (a): 180
If we substitute P = 180 in the equation, we can see that the left-hand side of the equation does not equal 16.
Option (b): 460
If we substitute P = 460 in the equation, we can see that the left-hand side of the equation does not equal 16.
Option (c): 520
If we substitute P = 520 in the equation, we can see that the left-hand side of the equation does not equal 16.
Option (d): 640
If we substitute P = 640 in the equation, we can see that the left-hand side of the equation equals 16.
Therefore, the correct option is (d) 640.
Hence, the Simple Interest is Rs. 640.
Note: It is important to verify the answer by substituting the value of P in the original equation to ensure it satisfies the given conditions.
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Community Answer
If the difference between the CI and SI on a sum of money at 5% per an...
The difference between compound interest nd the simple interest over two years is given by p(r/100)*(r/100).
so here p(5/100)*(5/100)=16
on solving for p we get , p=6400
....now by using the formula of simple interest we can find out the simple interest=ptr/100=6400*2*5/100=640
so here p(5/100)*(5/100)=16
on solving for p we get , p=6400
....now by using the formula of simple interest we can find out the simple interest=ptr/100=6400*2*5/100=640
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