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A person desires to create a fund to be invested at 10% CI per annum to provide for a prize of Rs. 300 every year. Using V = a/I find V and V will be
- a)Rs. 2000
- b)Rs. 2500
- c)Rs. 3000
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A person desires to create a fund to be invested at 10% CI per annum t...
Given:
- Annual prize = Rs. 300
- Interest rate = 10% per annum (Compound Interest)
- We need to find the value of the fund (V) using the formula V = a / I.
Step 1: Formula to Calculate Fund Value (V)
The formula to calculate the required fund value (V) is:
V = a / I
Where:
- a = Annual prize (Rs. 300)
- I = Interest on the fund per annum
Step 2: Interest Calculation
We know that the annual interest is 10% of the fund (V). So,
I = 0.10 * V
Step 3: Substitute the values into the formula
Now, substitute a = 300 and I = 0.10 * V into the formula:
V = 300 / (0.10 * V)
Step 4: Solve for V
Multiply both sides of the equation by 0.10 * V to eliminate the denominator:
0.10 * V * V = 300
This simplifies to:
0.10 * V2 = 300
Now, divide both sides by 0.10:
V2 = 3000
Now take the square root of both sides:
V = √3000 ≈ 54.77
Thus, the required fund value (V) is approximately Rs. 3000.
Conclusion:
The value of the fund needed to provide an annual prize of Rs. 300 is Rs. 3000.
C: Rs. 3000
Most Upvoted Answer
A person desires to create a fund to be invested at 10% CI per annum t...
Given data:
Principal amount (P) = ?
Rate of interest (R) = 10%
Time period (T) = ?
Amount of prize (A) = Rs. 300
We need to find the value of the principal amount (P) using the formula V = a/I, where V is the present value or principal amount, a is the amount of prize, and I is the interest rate.
Calculation:
As per the formula, V = a/I
Substituting the given values, we get:
V = 300/0.1 = Rs. 3000
Therefore, the correct option is (c) Rs. 3000.
Explanation:
The formula V = a/I is used to calculate the present value of a future cash flow, which takes into account the time value of money. In this case, the future cash flow is the annual prize of Rs. 300, which is received every year for an indefinite period.
To calculate the present value, we need to divide the annual prize by the interest rate expressed as a decimal. The resulting value gives us the present value or principal amount that should be invested at the given interest rate to generate the desired cash flow.
In this case, the interest rate is 10% per annum, which means that for every Rs. 100 invested, the return would be Rs. 10 per year. Therefore, to generate an annual prize of Rs. 300, we need to invest Rs. 3000 at 10% CI per annum.
Hence, the correct answer is Rs. 3000.
Principal amount (P) = ?
Rate of interest (R) = 10%
Time period (T) = ?
Amount of prize (A) = Rs. 300
We need to find the value of the principal amount (P) using the formula V = a/I, where V is the present value or principal amount, a is the amount of prize, and I is the interest rate.
Calculation:
As per the formula, V = a/I
Substituting the given values, we get:
V = 300/0.1 = Rs. 3000
Therefore, the correct option is (c) Rs. 3000.
Explanation:
The formula V = a/I is used to calculate the present value of a future cash flow, which takes into account the time value of money. In this case, the future cash flow is the annual prize of Rs. 300, which is received every year for an indefinite period.
To calculate the present value, we need to divide the annual prize by the interest rate expressed as a decimal. The resulting value gives us the present value or principal amount that should be invested at the given interest rate to generate the desired cash flow.
In this case, the interest rate is 10% per annum, which means that for every Rs. 100 invested, the return would be Rs. 10 per year. Therefore, to generate an annual prize of Rs. 300, we need to invest Rs. 3000 at 10% CI per annum.
Hence, the correct answer is Rs. 3000.
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A person desires to create a fund to be invested at 10% CI per annum t...
300/.1=3000
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A person desires to create a fund to be invested at 10% CI per annum to provide for a prize of Rs. 300 every year. Using V = a/I find V and V will bea)Rs. 2000b)Rs. 2500c)Rs. 3000d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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