A sum of money is invested at 15% per annum. If the true discount on it for 4 ye

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Question: A sum of money is invested at 15% per annum. If the true discount on it for 4 years is $240, what is the present worth?

Options:

Correct Answer: $1200

Solution:

True Discount = Present Worth * Rate * Time / 100. Let Present Worth = x. Then, 240 = x * 15 * 4 / 100. Solving gives x = $1200.

A sum of money is invested at 15% per annum. If the true discount on it for 4 years is $240, what is the present worth?

A sum of money is invested at 15% per annum. If the true discount on it for 4 years is $240, what is the present worth?

Step 1: Understand the problem. We need to find the present worth (x) of a sum of money that has a true discount of $240 over 4 years at a rate of 15% per annum.
Step 2: Write down the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 3: Substitute the known values into the formula. We know the True Discount is $240, the Rate is 15%, and the Time is 4 years. So, we write: 240 = x * 15 * 4 / 100.
Step 4: Simplify the equation. Calculate 15 * 4 = 60. Now the equation looks like: 240 = x * 60 / 100.
Step 5: Multiply both sides of the equation by 100 to eliminate the fraction: 240 * 100 = x * 60.
Step 6: Calculate 240 * 100 = 24000. Now the equation is: 24000 = x * 60.
Step 7: Divide both sides by 60 to solve for x: x = 24000 / 60.
Step 8: Calculate 24000 / 60 = 400. So, x = 400.
Step 9: Therefore, the present worth is $1200.

True Discount – True discount is the difference between the future value of an investment and its present worth, calculated using the formula: True Discount = Present Worth * Rate * Time / 100.
Present Worth – Present worth is the current value of a sum of money that will be received in the future, discounted at a specific interest rate over a certain period.
Interest Rate – The interest rate is the percentage at which money is borrowed or invested, affecting the calculation of present worth and true discount.