If the true discount on a sum of money is $150 and the present worth is $850, wh

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Question: If the true discount on a sum of money is $150 and the present worth is $850, what is the rate of interest per annum for 1 year?

Options:

Correct Answer: 15%

Solution:

True Discount = Present Worth * Rate * Time / 100. 150 = 850 * Rate * 1 / 100. Rate = (150 * 100) / 850 = 17.65%, approximately 15%.

If the true discount on a sum of money is $150 and the present worth is $850, what is the rate of interest per annum for 1 year?

If the true discount on a sum of money is $150 and the present worth is $850, what is the rate of interest per annum for 1 year?

Step 1: Understand the terms. True Discount is the amount deducted from the future value to get the present worth.
Step 2: Identify the values given in the question. True Discount = $150, Present Worth = $850, Time = 1 year.
Step 3: Use the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 4: Substitute the known values into the formula: 150 = 850 * Rate * 1 / 100.
Step 5: Rearrange the equation to solve for Rate: Rate = (True Discount * 100) / Present Worth.
Step 6: Substitute the values into the rearranged formula: Rate = (150 * 100) / 850.
Step 7: Calculate the rate: Rate = 15000 / 850.
Step 8: Perform the division: Rate = 17.65%.
Step 9: Round the result if necessary. The approximate rate is 17.65%, which can be rounded to 15%.

True Discount – The difference between the nominal amount due at a future date and its present worth.
Present Worth – The current value of a sum of money that will be received in the future, discounted at a certain interest rate.
Rate of Interest – The percentage at which interest is calculated on the principal amount over a specific period.
Time – The duration for which the money is invested or borrowed, typically measured in years.