If a sum of $3000 is due in 6 years at a rate of 9% per annum, what is the true

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Question: If a sum of $3000 is due in 6 years at a rate of 9% per annum, what is the true discount?

Options:

Correct Answer: $500

Solution:

Present Worth = 3000 / (1 + 0.09*6) = 3000 / 1.54 = $1948.05. True Discount = 3000 - 1948.05 = $1051.95.

If a sum of $3000 is due in 6 years at a rate of 9% per annum, what is the true discount?

If a sum of $3000 is due in 6 years at a rate of 9% per annum, what is the true discount?

Step 1: Identify the total amount due in the future, which is $3000.
Step 2: Identify the interest rate, which is 9% per annum.
Step 3: Identify the time period, which is 6 years.
Step 4: Convert the interest rate from percentage to decimal by dividing by 100. So, 9% becomes 0.09.
Step 5: Calculate the total interest for 6 years using the formula: Total Interest = Rate * Time. So, Total Interest = 0.09 * 6 = 0.54.
Step 6: Calculate the Present Worth (the value today) using the formula: Present Worth = Future Amount / (1 + Total Interest). So, Present Worth = 3000 / (1 + 0.54) = 3000 / 1.54.
Step 7: Perform the division: 3000 / 1.54 = $1948.05.
Step 8: Calculate the True Discount using the formula: True Discount = Future Amount - Present Worth. So, True Discount = 3000 - 1948.05.
Step 9: Perform the subtraction: 3000 - 1948.05 = $1051.95.

Present Worth Calculation – Understanding how to calculate the present worth of a future sum using the formula for present value.
True Discount – The difference between the future value and the present worth, representing the cost of waiting for the future payment.
Interest Rate Application – Applying the interest rate correctly over the specified time period to determine the present value.