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A sum of $2000 is due in 4 years. If the true discount is $400, what is the rate

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Question: A sum of $2000 is due in 4 years. If the true discount is $400, what is the rate of interest per annum?

Options:

  1. 5%
  2. 6%
  3. 7%
  4. 8%

Correct Answer: 5%

Solution: 

True Discount = Amount - Present Worth. Present Worth = 2000 - 400 = $1600. Using the formula, 400 = 1600 * Rate * 4 / 100. Solving gives Rate = 6.25%.

A sum of $2000 is due in 4 years. If the true discount is $400, what is the rate

Practice Questions

Q1
A sum of $2000 is due in 4 years. If the true discount is $400, what is the rate of interest per annum?
  1. 5%
  2. 6%
  3. 7%
  4. 8%

Questions & Step-by-Step Solutions

A sum of $2000 is due in 4 years. If the true discount is $400, what is the rate of interest per annum?
  • Step 1: Understand that the total amount due in 4 years is $2000.
  • Step 2: Recognize that the true discount is $400.
  • Step 3: Calculate the Present Worth (PW) using the formula: PW = Amount - True Discount.
  • Step 4: Substitute the values: PW = 2000 - 400 = $1600.
  • Step 5: Use the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
  • Step 6: Substitute the known values into the formula: 400 = 1600 * Rate * 4 / 100.
  • Step 7: Rearrange the equation to solve for Rate: Rate = (400 * 100) / (1600 * 4).
  • Step 8: Calculate the Rate: Rate = 40000 / 6400 = 6.25%.
  • Step 9: Conclude that the rate of interest per annum is 6.25%.
  • True Discount – The difference between the amount due and the present worth, representing the interest that would have been earned on the present worth over the time period.
  • 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 money is invested or borrowed, in this case, 4 years.
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