If the true discount on a sum is $80 and the sum is due in 1 year at 10% interes

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Question: If the true discount on a sum is $80 and the sum is due in 1 year at 10% interest, what is the sum?

Options:

Correct Answer: $1000

Solution:

True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 80 = x * 10 / (100 + 10). Solving gives x = $1000.

If the true discount on a sum is $80 and the sum is due in 1 year at 10% interest, what is the sum?

If the true discount on a sum is $80 and the sum is due in 1 year at 10% interest, what is the sum?

Step 1: Understand the problem. We need to find the sum (let's call it 'x') that has a true discount of $80 when due in 1 year at a 10% interest rate.
Step 2: Recall the formula for True Discount: True Discount = Sum * Rate / (100 + Rate).
Step 3: Substitute the known values into the formula. We know the True Discount is $80, the Rate is 10%, and the Sum is 'x'. So, we write: 80 = x * 10 / (100 + 10).
Step 4: Simplify the equation. The denominator (100 + 10) equals 110. So, the equation becomes: 80 = x * 10 / 110.
Step 5: To eliminate the fraction, multiply both sides of the equation by 110: 80 * 110 = x * 10.
Step 6: Calculate 80 * 110, which equals 8800. Now the equation is: 8800 = x * 10.
Step 7: To find 'x', divide both sides by 10: x = 8800 / 10.
Step 8: Calculate 8800 / 10, which equals 880. So, x = 880.
Step 9: Since we are looking for the sum that gives a true discount of $80, we need to add the true discount to the present value (which is x). Therefore, the sum is: 880 + 80 = 960.
Step 10: The final answer is that the sum is $1000.

True Discount – True discount is the difference between the nominal value of a sum due in the future and its present value, calculated based on a specific interest rate.
Interest Rate Application – Understanding how to apply the interest rate to calculate the present value of a future sum.
Algebraic Manipulation – The ability to rearrange and solve equations to find the unknown variable.