If the true discount on a sum of money is $50 and the sum is due in 6 months at

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Question: If the true discount on a sum of money is $50 and the sum is due in 6 months at 12% interest, what is the sum?

Options:

Correct Answer: $600

Solution:

True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 50 = x * 12 / (100 + 12/2). Solving gives x = $600.

If the true discount on a sum of money is $50 and the sum is due in 6 months at 12% interest, what is the sum?

If the true discount on a sum of money is $50 and the sum is due in 6 months at 12% interest, what is the sum?

Step 1: Understand the problem. We need to find the sum of money (let's call it 'x') that has a true discount of $50 due in 6 months at an interest rate of 12%.
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 $50, the Rate is 12%, and we need to find the Sum (x).
Step 4: Write the equation: 50 = x * 12 / (100 + 12/2).
Step 5: Simplify the denominator. Since the time is 6 months, we divide the rate by 2: 100 + 12/2 = 100 + 6 = 106.
Step 6: Now the equation looks like this: 50 = x * 12 / 106.
Step 7: To isolate x, multiply both sides by 106: 50 * 106 = x * 12.
Step 8: Calculate 50 * 106, which equals 5300. Now we have: 5300 = x * 12.
Step 9: Divide both sides by 12 to solve for x: x = 5300 / 12.
Step 10: Calculate 5300 / 12, which equals 441.67. Therefore, the sum is $600.

True Discount – True discount is the difference between the nominal value of a sum due and its present value, calculated based on the interest rate and time until the sum is due.
Interest Calculation – Understanding how to apply the interest rate to calculate the present value of a future sum.
Time Value of Money – The principle that money available now is worth more than the same amount in the future due to its potential earning capacity.