A sum of $800 is due in 2 years. If the true discount is $160, what is the rate

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Question: A sum of $800 is due in 2 years. If the true discount is $160, what is the rate of interest?

Options:

Correct Answer: 7%

Solution:

True Discount = Amount - Present Worth. Present Worth = 800 - 160 = 640. Using the formula, 160 = 640 * r * 2 / 100. Solving gives r = 12.5%.

A sum of $800 is due in 2 years. If the true discount is $160, what is the rate of interest?

A sum of $800 is due in 2 years. If the true discount is $160, what is the rate of interest?

Step 1: Understand that the total amount due in 2 years is $800.
Step 2: Recognize that the true discount is $160.
Step 3: Calculate the Present Worth (PW) using the formula: PW = Amount - True Discount.
Step 4: Substitute the values: PW = 800 - 160 = 640.
Step 5: Use the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 6: Substitute the known values into the formula: 160 = 640 * r * 2 / 100.
Step 7: Rearrange the equation to solve for r: r = (160 * 100) / (640 * 2).
Step 8: Calculate the value: r = 16000 / 1280 = 12.5%.
Step 9: Conclude that the rate of interest is 12.5%.

True Discount – The difference between the amount due and the present worth, which reflects the interest that would have been earned over time.
Present Worth – The current value of a future sum of money, calculated by subtracting the true discount from the amount due.
Interest Rate Calculation – The process of determining the rate of interest based on the true discount, present worth, and time period.