If the true discount on a sum of money is $250 for 4 years at 5% per annum, what

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Question: If the true discount on a sum of money is $250 for 4 years at 5% per annum, what is the present worth?

Options:

Correct Answer: $2000

Solution:

True Discount = Present Worth * Rate * Time / 100. Let Present Worth = P. Then, 250 = P * 5 * 4 / 100. Solving gives P = $1250.

If the true discount on a sum of money is $250 for 4 years at 5% per annum, what is the present worth?

If the true discount on a sum of money is $250 for 4 years at 5% per annum, what is the present worth?

Step 1: Understand the formula for True Discount, which is: True Discount = Present Worth * Rate * Time / 100.
Step 2: Identify the values given in the question: True Discount = $250, Rate = 5%, Time = 4 years.
Step 3: Substitute the known values into the formula: 250 = Present Worth * 5 * 4 / 100.
Step 4: Simplify the equation: 250 = Present Worth * 20 / 100.
Step 5: Multiply both sides by 100 to eliminate the fraction: 250 * 100 = Present Worth * 20.
Step 6: Calculate the left side: 25000 = Present Worth * 20.
Step 7: Divide both sides by 20 to solve for Present Worth: Present Worth = 25000 / 20.
Step 8: Calculate the final value: Present Worth = 1250.

True Discount – The difference between the nominal amount due at a future date 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 at a specific interest rate over a certain period.
Interest Rate Calculation – Understanding how to apply the interest rate in the context of time to calculate present worth or true discount.