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

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

Options:

Correct Answer: $2000

Solution:

Let Present Worth = x. True Discount = x * 5 * 4 / 100. Thus, 250 = x * 20 / 100. Solving gives x = $1250.

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

If the true discount on a sum of money is $250 at 5% per annum for 4 years, 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 = $250, rate = 5% per annum, time = 4 years.
Step 3: Use the formula for true discount: True Discount = Present Worth * Rate * Time / 100.
Step 4: Substitute the known values into the formula: 250 = x * 5 * 4 / 100.
Step 5: Simplify the equation: 250 = x * 20 / 100.
Step 6: Multiply both sides by 100 to eliminate the fraction: 25000 = x * 20.
Step 7: Divide both sides by 20 to solve for x: x = 25000 / 20.
Step 8: Calculate the value: x = 1250.
Step 9: Conclude that the present worth is $1250.

True Discount – The difference between the nominal amount and the 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 to calculate the true discount and present worth.