A sum of $5000 is due in 3 years. If the rate of interest is 5% per annum, what

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Question: A sum of $5000 is due in 3 years. If the rate of interest is 5% per annum, what is the true discount?

Options:

$500
$600
$700
$800

Correct Answer: $500

Solution:

True Discount = Amount - Present Worth. Present Worth = Amount / (1 + rt) = 5000 / (1 + 0.05*3) = 5000 / 1.15 = $4347.83. True Discount = 5000 - 4347.83 = $652.17.

A sum of $5000 is due in 3 years. If the rate of interest is 5% per annum, what

Practice Questions

A sum of $5000 is due in 3 years. If the rate of interest is 5% per annum, what is the true discount?

$500
$600
$700
$800

Questions & Step-by-Step Solutions

A sum of $5000 is due in 3 years. If the rate of interest is 5% per annum, what is the true discount?

Step 1: Identify the total amount due, which is $5000.
Step 2: Identify the interest rate, which is 5% per annum.
Step 3: Identify the time period, which is 3 years.
Step 4: Convert the interest rate from percentage to decimal by dividing by 100. So, 5% becomes 0.05.
Step 5: Calculate the total interest for 3 years using the formula: Interest = Principal × Rate × Time. Here, Principal is the amount due ($5000), Rate is 0.05, and Time is 3 years.
Step 6: Calculate the Present Worth (PW) using the formula: Present Worth = Amount / (1 + rt), where r is the rate and t is the time. Substitute the values: PW = 5000 / (1 + 0.05 * 3).
Step 7: Calculate (1 + 0.05 * 3) = 1 + 0.15 = 1.15.
Step 8: Now calculate Present Worth: PW = 5000 / 1.15 = $4347.83.
Step 9: Calculate the True Discount using the formula: True Discount = Amount - Present Worth. Substitute the values: True Discount = 5000 - 4347.83.
Step 10: Calculate the True Discount: True Discount = $652.17.

True Discount – The difference between the future amount due and its present worth, calculated using the interest rate and time.
Present Worth – The current value of a future sum of money, discounted back to the present using the interest rate.
Interest Calculation – Understanding how to apply the formula for calculating present worth using simple interest.

A sum of $5000 is due in 3 years. If the rate of interest is 5% per annum, what

What’s inside this PDF?

A sum of $5000 is due in 3 years. If the rate of interest is 5% per annum, what

Practice Questions

Questions & Step-by-Step Solutions

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