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

₹0.0

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

Options:

Correct Answer: 10%

Solution:

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

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

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

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 * Rate * 2 / 100.
Step 7: Rearrange the equation to solve for Rate: Rate = (160 * 100) / (640 * 2).
Step 8: Calculate the Rate: Rate = 16000 / 1280 = 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.
Rate of Interest – The percentage at which interest is calculated on the present worth over a specified time period.
Time Period – The duration for which the interest is calculated, in this case, 2 years.