If the present worth of a sum is $600 and the true discount is $150 for 3 years,

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Question: If the present worth of a sum is $600 and the true discount is $150 for 3 years, what is the rate of interest?

Options:

Correct Answer: 7%

Solution:

True Discount = Present Worth * Rate * Time / 100. Thus, 150 = 600 * r * 3 / 100. Solving gives r = 8%.

If the present worth of a sum is $600 and the true discount is $150 for 3 years, what is the rate of interest?

If the present worth of a sum is $600 and the true discount is $150 for 3 years, what is the rate of interest?

Step 1: Understand the terms. Present Worth is the current value of a sum of money, which is $600 in this case.
Step 2: Know what True Discount means. True Discount is the amount deducted from the future sum to get the Present Worth, which is $150 here.
Step 3: Identify the time period. The time period given is 3 years.
Step 4: Use the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 5: Substitute the known values into the formula: 150 = 600 * r * 3 / 100.
Step 6: Rearrange the equation to solve for r (rate): r = (150 * 100) / (600 * 3).
Step 7: Calculate the right side: r = 15000 / 1800.
Step 8: Simplify the fraction: r = 8.33.
Step 9: Convert to percentage: r = 8.33%, which can be rounded to 8%.

Present Worth – The current value of a future sum of money, discounted at a specific interest rate.
True Discount – The difference between the future value and the present worth, representing the cost of borrowing.
Rate of Interest – The percentage at which interest is charged or paid on a sum of money.
Time – The duration for which the money is borrowed or invested, typically measured in years.