If the true discount on a sum is $150 and the sum is due in 1 year at 5% interes

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Question: If the true discount on a sum is $150 and the sum is due in 1 year at 5% interest, what is the sum?

Options:

Correct Answer: $2500

Solution:

True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 150 = x * 5 / (100 + 5). Solving gives x = $2500.

If the true discount on a sum is $150 and the sum is due in 1 year at 5% interest, what is the sum?

If the true discount on a sum is $150 and the sum is due in 1 year at 5% 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 $150 when due in 1 year at 5% interest.
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 $150 and the Rate is 5%. So, we write: 150 = x * 5 / (100 + 5).
Step 4: Simplify the equation. The denominator (100 + 5) is 105, so we rewrite the equation as: 150 = x * 5 / 105.
Step 5: To eliminate the fraction, multiply both sides of the equation by 105: 150 * 105 = x * 5.
Step 6: Calculate 150 * 105, which equals 15750. Now we have: 15750 = x * 5.
Step 7: To find x, divide both sides by 5: x = 15750 / 5.
Step 8: Calculate 15750 / 5, which equals 3150. So, x = 3150.
Step 9: Therefore, the sum is $3150.

True Discount – True discount is the difference between the nominal value of a sum due in the future and its present value, calculated using the interest rate.
Interest Calculation – Understanding how to apply the interest rate to calculate the present value of a future sum.
Algebraic Manipulation – Ability to rearrange and solve equations to find the unknown variable.