A loan of $5000 is taken for 3 years at a certain rate of interest. If the true

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Question: A loan of $5000 is taken for 3 years at a certain rate of interest. If the true discount is $600, what is the rate of interest?

Options:

Correct Answer: 6%

Solution:

True Discount = Present Worth * Rate * Time / 100. 600 = 5000 * Rate * 3 / 100. Rate = (600 * 100) / (5000 * 3) = 4%.

A loan of $5000 is taken for 3 years at a certain rate of interest. If the true discount is $600, what is the rate of interest?

A loan of $5000 is taken for 3 years at a certain rate of interest. If the true discount is $600, what is the rate of interest?

Step 1: Understand the problem. We have a loan of $5000 for 3 years and a true discount of $600. We need to find the rate of interest.
Step 2: Recall the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 3: Identify the values in the formula. Here, True Discount is $600, Present Worth is $5000, and Time is 3 years.
Step 4: Substitute the known values into the formula: 600 = 5000 * Rate * 3 / 100.
Step 5: Rearrange the equation to solve for Rate. Multiply both sides by 100: 600 * 100 = 5000 * Rate * 3.
Step 6: Simplify the left side: 60000 = 5000 * Rate * 3.
Step 7: Divide both sides by (5000 * 3) to isolate Rate: Rate = 60000 / (5000 * 3).
Step 8: Calculate the denominator: 5000 * 3 = 15000.
Step 9: Now calculate Rate: Rate = 60000 / 15000.
Step 10: Simplify the fraction: Rate = 4.
Step 11: Conclude that the rate of interest is 4%.

True Discount – True discount is the difference between the nominal value of a loan and its present worth, calculated based on the interest rate and time.
Present Worth – Present worth refers to the current value of a future sum of money or stream of cash flows given a specified rate of return.
Rate of Interest – The rate of interest is the percentage at which interest is calculated on the principal amount of a loan.
Time Factor – Time factor in interest calculations refers to the duration for which the money is borrowed or invested.