A sum of $2000 is due in 3 years. If the true discount is $300, what is the rate

₹0.0

Question: A sum of $2000 is due in 3 years. If the true discount is $300, what is the rate of interest?

Options:

Correct Answer: 5%

Solution:

Present Worth = 2000 - 300 = 1700. Using the formula, 300 = 1700 * r * 3 / 100. Solving gives r = 5.29%.

A sum of $2000 is due in 3 years. If the true discount is $300, what is the rate of interest?

A sum of $2000 is due in 3 years. If the true discount is $300, what is the rate of interest?

Step 1: Identify the total amount due in the future, which is $2000.
Step 2: Identify the true discount, which is $300.
Step 3: Calculate the Present Worth by subtracting the true discount from the total amount due: Present Worth = 2000 - 300 = 1700.
Step 4: Use the formula for true discount: True Discount = Present Worth * Rate * Time / 100.
Step 5: Substitute the known values into the formula: 300 = 1700 * r * 3 / 100.
Step 6: Rearrange the formula to solve for r: r = (300 * 100) / (1700 * 3).
Step 7: Calculate the value of r: r = 30000 / 5100 = 5.29%.
Step 8: Conclude that the rate of interest is 5.29%.

True Discount – The amount deducted from the future sum to find the present worth.
Present Worth – The current value of a future sum of money, calculated by subtracting the true discount from the future sum.
Interest Rate Calculation – The process of determining the rate of interest based on the present worth, future sum, and time period.