If the true discount on a sum of money is $100 for 3 years at 6% per annum, what

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Question: If the true discount on a sum of money is $100 for 3 years at 6% per annum, what is the sum?

Options:

Correct Answer: $1800

Solution:

True Discount = Present Worth * Rate * Time / 100. Let Present Worth = P. Then, 100 = P * 6 * 3 / 100. Solving gives P = $555.56, thus Sum = $655.56.

If the true discount on a sum of money is $100 for 3 years at 6% per annum, what is the sum?

If the true discount on a sum of money is $100 for 3 years at 6% per annum, what is the sum?

Step 1: Understand the terms. True Discount is the amount deducted from the sum to find the Present Worth.
Step 2: Identify the given values. True Discount is $100, Time is 3 years, and Rate is 6% per annum.
Step 3: Write the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 4: Let Present Worth be represented as P. Substitute the known values into the formula: 100 = P * 6 * 3 / 100.
Step 5: Simplify the equation: 100 = P * 18 / 100.
Step 6: Multiply both sides by 100 to eliminate the fraction: 10000 = P * 18.
Step 7: Divide both sides by 18 to solve for P: P = 10000 / 18.
Step 8: Calculate P: P = $555.56 (approximately).
Step 9: Find the Sum by adding the True Discount to the Present Worth: Sum = P + True Discount = 555.56 + 100.
Step 10: Calculate the Sum: Sum = $655.56.

True Discount – True discount is the difference between the sum due at a future date and its present worth, calculated based on the interest rate and time period.
Present Worth – Present worth is the current value of a future sum of money, discounted at a specific interest rate over a certain period.
Interest Calculation – Understanding how to calculate interest and apply it to find present worth and future sums.