If the true discount on a sum of money is $50 at 10% per annum for 2 years, what

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Question: If the true discount on a sum of money is $50 at 10% per annum for 2 years, what is the present worth?

Options:

Correct Answer: $500

Solution:

Let Present Worth = x. True Discount = x * 10 * 2 / 100. Thus, 50 = x * 20 / 100. Solving gives x = $250.

If the true discount on a sum of money is $50 at 10% per annum for 2 years, what is the present worth?

If the true discount on a sum of money is $50 at 10% per annum for 2 years, what is the present worth?

Step 1: Understand that the true discount is the amount deducted from the future value to get the present worth.
Step 2: Let the present worth be represented by 'x'.
Step 3: The formula for true discount is: True Discount = Present Worth * Rate * Time / 100.
Step 4: Substitute the known values into the formula: True Discount = x * 10 * 2 / 100.
Step 5: We know the true discount is $50, so set up the equation: 50 = x * 20 / 100.
Step 6: Simplify the equation: 50 = x * 0.2.
Step 7: To find 'x', divide both sides by 0.2: x = 50 / 0.2.
Step 8: Calculate the value: x = 250.
Step 9: Therefore, the present worth is $250.

True Discount – The difference between the nominal value of a sum of money and its present worth, calculated based on a specific interest rate and time period.
Present Worth – The current value of a future sum of money, discounted back to the present using a specific interest rate.
Interest Rate Calculation – Understanding how to apply the interest rate to calculate true discount and present worth.