A sum of $3000 is due in 2 years. If the rate of interest is 6% per annum, what

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Question: A sum of $3000 is due in 2 years. If the rate of interest is 6% per annum, what is the true discount?

Options:

Correct Answer: $300

Solution:

Present Worth = Amount / (1 + rt) = 3000 / (1 + 0.06*2) = 3000 / 1.12 = $2678.57. True Discount = 3000 - 2678.57 = $321.43.

A sum of $3000 is due in 2 years. If the rate of interest is 6% per annum, what is the true discount?

A sum of $3000 is due in 2 years. If the rate of interest is 6% per annum, what is the true discount?

Step 1: Identify the total amount due, which is $3000.
Step 2: Identify the interest rate, which is 6% per annum.
Step 3: Identify the time period, which is 2 years.
Step 4: Convert the interest rate from percentage to decimal by dividing by 100. So, 6% becomes 0.06.
Step 5: Calculate the total interest for 2 years using the formula: Interest = Principal × Rate × Time. Here, Principal is the amount due ($3000), Rate is 0.06, and Time is 2 years.
Step 6: Calculate the total interest: Interest = 3000 × 0.06 × 2 = $360.
Step 7: Calculate the Present Worth (PW) using the formula: PW = Amount / (1 + rt). Substitute the values: PW = 3000 / (1 + 0.06 * 2).
Step 8: Calculate the denominator: 1 + (0.06 * 2) = 1 + 0.12 = 1.12.
Step 9: Now calculate the Present Worth: PW = 3000 / 1.12 = $2678.57.
Step 10: Calculate the True Discount using the formula: True Discount = Amount - Present Worth. Substitute the values: True Discount = 3000 - 2678.57.
Step 11: Calculate the True Discount: True Discount = $321.43.

Present Worth Calculation – Understanding how to calculate the present value of a future sum using the formula Present Worth = Amount / (1 + rt).
True Discount – Calculating the true discount as the difference between the future amount and its present worth.
Interest Rate Application – Applying the interest rate correctly over the specified time period to determine the present worth.