A sum of money is invested at 8% per annum. If the true discount on it for 2 yea

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Question: A sum of money is invested at 8% per annum. If the true discount on it for 2 years is $160, what is the present worth?

Options:

Correct Answer: $1000

Solution:

True Discount = Present Worth * Rate * Time / 100. Let Present Worth = x. Then, 160 = x * 8 * 2 / 100. Solving gives x = $1000.

A sum of money is invested at 8% per annum. If the true discount on it for 2 years is $160, what is the present worth?

A sum of money is invested at 8% per annum. If the true discount on it for 2 years is $160, what is the present worth?

Step 1: Understand the problem. We need to find the present worth (x) of a sum of money that has a true discount of $160 over 2 years at an interest rate of 8% per annum.
Step 2: Write down the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 3: Substitute the known values into the formula. We know the True Discount is $160, the Rate is 8%, and the Time is 2 years. So, we write: 160 = x * 8 * 2 / 100.
Step 4: Simplify the equation. Calculate 8 * 2 = 16. Now the equation looks like: 160 = x * 16 / 100.
Step 5: Multiply both sides of the equation by 100 to eliminate the fraction: 160 * 100 = x * 16.
Step 6: Calculate 160 * 100 = 16000. Now the equation is: 16000 = x * 16.
Step 7: Divide both sides by 16 to solve for x: x = 16000 / 16.
Step 8: Calculate 16000 / 16 = 1000. Therefore, the present worth (x) is $1000.

True Discount – True discount is the difference between the nominal amount and the present worth, calculated based on the interest rate and time.
Present Worth – Present worth is the current value of a future sum of money, discounted at a specific interest rate over a certain period.
Interest Rate Calculation – Understanding how to apply the interest rate in the context of true discount calculations.