A sum of money is invested at a rate of 6% per annum. If the true discount on th

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Question: A sum of money is invested at a rate of 6% per annum. If the true discount on the sum for 5 years is $500, what is the sum?

Options:

$3000
$3500
$4000
$4500

Correct Answer: $4000

Solution:

Let the sum be x. True Discount = x * 6 * 5 / 100. Thus, 500 = x * 30 / 100. Solving gives x = $1666.67. Therefore, the sum = $1666.67 + $500 = $2166.67.

A sum of money is invested at a rate of 6% per annum. If the true discount on th

Practice Questions

A sum of money is invested at a rate of 6% per annum. If the true discount on the sum for 5 years is $500, what is the sum?

$3000
$3500
$4000
$4500

Questions & Step-by-Step Solutions

A sum of money is invested at a rate of 6% per annum. If the true discount on the sum for 5 years is $500, what is the sum?

Step 1: Understand that we need to find the original sum of money, which we will call 'x'.
Step 2: Know that the true discount is the amount of money saved by not having to pay interest on the sum for a certain period.
Step 3: The formula for true discount is: True Discount = (Sum * Rate * Time) / 100.
Step 4: In this case, the rate is 6% per annum, and the time is 5 years.
Step 5: Substitute the values into the formula: True Discount = (x * 6 * 5) / 100.
Step 6: We know the true discount is $500, so we set up the equation: 500 = (x * 30) / 100.
Step 7: To eliminate the fraction, multiply both sides of the equation by 100: 500 * 100 = x * 30.
Step 8: This simplifies to: 50000 = 30x.
Step 9: Now, solve for x by dividing both sides by 30: x = 50000 / 30.
Step 10: Calculate x, which gives x = $1666.67.
Step 11: The true discount of $500 is the amount saved, so to find the total sum, add the true discount to x: Total Sum = x + True Discount.
Step 12: Therefore, Total Sum = $1666.67 + $500 = $2166.67.

True Discount – True discount is the difference between the present value and the future value of a sum of money, calculated based on the interest rate and time period.
Simple Interest – The calculation of interest on a principal sum over a specified period, typically expressed as a percentage of the principal.
Present Value and Future Value – Understanding the relationship between present value, future value, and the time value of money is crucial for solving investment problems.

A sum of money is invested at a rate of 6% per annum. If the true discount on th

What’s inside this PDF?

A sum of money is invested at a rate of 6% per annum. If the true discount on th

Practice Questions

Questions & Step-by-Step Solutions

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