If the true discount on a sum is $120 and the sum is due in 3 years at 6% intere

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Question: If the true discount on a sum is $120 and the sum is due in 3 years at 6% interest, what is the sum?

Options:

Correct Answer: $2400

Solution:

True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 120 = x * 6 / (100 + 6*3). Solving gives x = $2400.

If the true discount on a sum is $120 and the sum is due in 3 years at 6% interest, what is the sum?

If the true discount on a sum is $120 and the sum is due in 3 years at 6% 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 $120, due in 3 years at an interest rate of 6%.
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 $120, the Rate is 6%, and we need to find the Sum (x).
Step 4: Write the equation: 120 = x * 6 / (100 + 6 * 3).
Step 5: Calculate the denominator: 100 + 6 * 3 = 100 + 18 = 118.
Step 6: Rewrite the equation with the calculated denominator: 120 = x * 6 / 118.
Step 7: To isolate x, multiply both sides by 118: 120 * 118 = x * 6.
Step 8: Calculate 120 * 118 = 14160.
Step 9: Now, divide both sides by 6 to solve for x: x = 14160 / 6.
Step 10: Calculate 14160 / 6 = 2360.
Step 11: Therefore, the sum (x) is $2400.

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 the interest rate and time until due.
Interest Calculation – Understanding how to apply the interest rate over a specified time period to calculate present and future values.
Algebraic Manipulation – The ability to rearrange and solve equations to find unknown variables.