If the present worth of a sum is $800 and the true discount is $200 for 2 years,

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Question: If the present worth of a sum is $800 and the true discount is $200 for 2 years, what is the rate of interest?

Options:

Correct Answer: 12.5%

Solution:

True Discount = Present Worth * Rate * Time / 100. Thus, 200 = 800 * r * 2 / 100. Solving gives r = 12.5%.

If the present worth of a sum is $800 and the true discount is $200 for 2 years, what is the rate of interest?

If the present worth of a sum is $800 and the true discount is $200 for 2 years, what is the rate of interest?

Step 1: Understand the terms. Present Worth is the current value of a sum of money, which is $800 in this case.
Step 2: Know that True Discount is the amount deducted from the future value to get the present worth. Here, the True Discount is $200.
Step 3: Identify the time period involved, which is 2 years.
Step 4: Use the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 5: Substitute the known values into the formula: 200 = 800 * r * 2 / 100.
Step 6: Simplify the equation: 200 = 800 * r * 0.02.
Step 7: Calculate 800 * 0.02, which equals 16. So, the equation becomes 200 = 16 * r.
Step 8: Solve for r by dividing both sides by 16: r = 200 / 16.
Step 9: Calculate 200 / 16, which equals 12.5.
Step 10: Conclude that the rate of interest is 12.5%.

Present Worth – The current value of a future sum of money, discounted at a specific interest rate.
True Discount – The difference between the future value and the present worth, representing the interest that would have been earned over time.
Rate of Interest – The percentage at which interest is calculated on the principal amount over a specific period.
Time Factor – The duration for which the money is invested or borrowed, typically expressed in years.