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

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

Options:

Correct Answer: $500

Solution:

True Discount = Present Worth * Rate * Time / 100. Let Present Worth = P. Then, 50 = P * 10 * 2 / 100. Solving gives P = $250.

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

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

Step 1: Understand the terms. True discount is the amount deducted from the future value to get the present worth.
Step 2: Identify the given values. True discount = $50, Rate = 10%, Time = 2 years.
Step 3: Write the formula for true discount: True Discount = Present Worth * Rate * Time / 100.
Step 4: Let Present Worth be represented as P.
Step 5: Substitute the known values into the formula: 50 = P * 10 * 2 / 100.
Step 6: Simplify the equation: 50 = P * 20 / 100.
Step 7: Multiply both sides by 100 to eliminate the fraction: 5000 = P * 20.
Step 8: Divide both sides by 20 to solve for P: P = 5000 / 20.
Step 9: Calculate the value: P = 250.
Step 10: Conclude that the present worth is $250.

True Discount – True discount is the difference between the future value and the present worth, calculated based on the interest rate and time period.
Present Worth – Present worth is the current value of a sum of money that will be received in the future, discounted back to the present using a specific interest rate.
Interest Rate Calculation – Understanding how to apply the interest rate in the context of time to calculate present worth from true discount.