A sum of money is invested at a rate of 8% per annum. If the true discount on th

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Question: A sum of money is invested at a rate of 8% per annum. If the true discount on the sum for 5 years is $400, what is the sum?

Options:

Correct Answer: $2000

Solution:

Let the sum be x. True Discount = x * 8 * 5 / 100. Thus, 400 = x * 40 / 100. Solving gives x = $1000. Therefore, the sum = $1000 + $400 = $1400.

A sum of money is invested at a rate of 8% per annum. If the true discount on the sum for 5 years is $400, what is the sum?

A sum of money is invested at a rate of 8% per annum. If the true discount on the sum for 5 years is $400, what is the sum?

Step 1: Understand that we need to find the total 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 the full sum right away. In this case, the true discount for 5 years is $400.
Step 3: The formula for true discount is: True Discount = (Sum * Rate * Time) / 100.
Step 4: Substitute the known values into the formula: 400 = (x * 8 * 5) / 100.
Step 5: Simplify the equation: 400 = (x * 40) / 100.
Step 6: Multiply both sides by 100 to eliminate the fraction: 40000 = x * 40.
Step 7: Divide both sides by 40 to solve for x: x = 40000 / 40.
Step 8: Calculate x: x = 1000. This means the sum is $1000.
Step 9: Add the true discount to the sum to find the total amount: Total Sum = 1000 + 400.
Step 10: Calculate the total sum: Total Sum = 1400.

True Discount – The amount deducted from the sum due to the interest rate over a specific period.
Simple Interest Calculation – Understanding how to calculate interest over time using the formula for simple interest.
Present Value and Future Value – The relationship between the present value of an investment and its future value considering interest.