True Discount MCQ & Objective Questions
Understanding the concept of True Discount is crucial for students preparing for various exams. This topic not only enhances your mathematical skills but also plays a significant role in scoring better in objective questions. By practicing True Discount MCQs and other practice questions, you can solidify your grasp on important concepts and improve your exam preparation strategy.
What You Will Practise Here
Definition and significance of True Discount
Formulas related to True Discount calculations
Difference between True Discount and other types of discounts
Real-life applications of True Discount in financial scenarios
Sample problems and solutions on True Discount
Diagrams illustrating the concept of True Discount
Commonly asked True Discount questions in exams
Exam Relevance
The topic of True Discount is frequently included in the syllabus for CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to calculate True Discount based on given values or to differentiate between various types of discounts. Common question patterns include direct calculation problems and conceptual questions that test your understanding of the underlying principles.
Common Mistakes Students Make
Confusing True Discount with Simple Discount
Incorrect application of formulas during calculations
Overlooking the importance of understanding the context of the problem
Failing to convert percentages into decimal form correctly
FAQs
Question: What is True Discount?Answer: True Discount is the actual reduction in the price of an item, calculated based on the present value of future cash flows.
Question: How do I calculate True Discount?Answer: True Discount can be calculated using the formula: True Discount = (Present Value x Rate x Time) / 100.
Now is the time to enhance your understanding of True Discount! Dive into our practice MCQs and test your knowledge to ensure you are well-prepared for your exams. Remember, consistent practice is the key to success!
Q. 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?
Show solution
Solution
True Discount = Present Worth * Rate * Time / 100. 600 = 5000 * Rate * 3 / 100. Rate = (600 * 100) / (5000 * 3) = 4%.
Correct Answer:
C
— 6%
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Q. A sum of $2000 is due in 3 years. If the true discount is $300, what is the rate of interest?
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Solution
Present Worth = 2000 - 300 = 1700. Using the formula, 300 = 1700 * r * 3 / 100. Solving gives r = 5.29%.
Correct Answer:
B
— 5%
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Q. A sum of $2000 is due in 4 years. If the true discount is $400, what is the rate of interest per annum?
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Solution
True Discount = Amount - Present Worth. Present Worth = 2000 - 400 = $1600. Using the formula, 400 = 1600 * Rate * 4 / 100. Solving gives Rate = 6.25%.
Correct Answer:
A
— 5%
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Q. A sum of $3000 is due in 2 years. If the rate of interest is 6% per annum, what is the true discount?
A.
$200
B.
$300
C.
$400
D.
$500
Show solution
Solution
Present Worth = Amount / (1 + rt) = 3000 / (1 + 0.06*2) = 3000 / 1.12 = $2678.57. True Discount = 3000 - 2678.57 = $321.43.
Correct Answer:
B
— $300
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Q. A sum of $5000 is due in 3 years. If the rate of interest is 5% per annum, what is the true discount?
A.
$500
B.
$600
C.
$700
D.
$800
Show solution
Solution
True Discount = Amount - Present Worth. Present Worth = Amount / (1 + rt) = 5000 / (1 + 0.05*3) = 5000 / 1.15 = $4347.83. True Discount = 5000 - 4347.83 = $652.17.
Correct Answer:
A
— $500
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Q. A sum of $800 is due in 2 years. If the true discount is $160, what is the rate of interest?
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Solution
True Discount = Amount - Present Worth. Present Worth = 800 - 160 = 640. Using the formula, 160 = 640 * r * 2 / 100. Solving gives r = 12.5%.
Correct Answer:
C
— 7%
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Q. A sum of $800 is due in 2 years. If the true discount is $160, what is the rate of interest per annum?
A.
8%
B.
10%
C.
12%
D.
15%
Show solution
Solution
True Discount = Amount - Present Worth. Present Worth = 800 - 160 = $640. Using the formula, 160 = 640 * Rate * 2 / 100. Solving gives Rate = 12.5%.
Correct Answer:
B
— 10%
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Q. A sum of money amounts to $1200 in 2 years at a rate of 8% per annum. What is the true discount?
A.
$100
B.
$120
C.
$150
D.
$180
Show solution
Solution
Present Worth = Amount / (1 + rt) = 1200 / (1 + 0.08*2) = 1200 / 1.16 = $1034.48. True Discount = 1200 - 1034.48 = $165.52.
Correct Answer:
B
— $120
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Q. A sum of money amounts to $1200 in 3 years at a certain rate of interest. If the true discount is $300, what is the rate of interest?
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Solution
Let the present worth be x. Then, x + 300 = 1200, so x = 900. True Discount = x * Rate * Time / 100. 300 = 900 * Rate * 3 / 100. Rate = 10%.
Correct Answer:
B
— 6%
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Q. A sum of money amounts to $1200 in 3 years at a certain rate of interest. If the true discount is $300, what is the present worth?
A.
$900
B.
$1000
C.
$1100
D.
$1200
Show solution
Solution
Present Worth = Amount - True Discount. Therefore, Present Worth = 1200 - 300 = $900.
Correct Answer:
A
— $900
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Q. A sum of money amounts to $1500 after 2 years at a certain rate of interest. If the true discount is $300, what is the present worth?
A.
$1200
B.
$1300
C.
$1400
D.
$1500
Show solution
Solution
Present Worth = Amount - True Discount. Therefore, Present Worth = 1500 - 300 = $1200.
Correct Answer:
A
— $1200
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Q. A sum of money amounts to $1500 after 4 years at a certain rate of interest. If the true discount is $300, what is the present worth?
A.
$1200
B.
$1300
C.
$1400
D.
$1500
Show solution
Solution
Present Worth = Amount - True Discount. Thus, Present Worth = 1500 - 300 = $1200.
Correct Answer:
A
— $1200
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Q. A sum of money amounts to $1500 after 5 years. If the true discount is $300, what is the present worth?
A.
$1200
B.
$1300
C.
$1400
D.
$1500
Show solution
Solution
Present Worth = Amount - True Discount = 1500 - 300 = $1200.
Correct Answer:
A
— $1200
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Q. A sum of money amounts to $1500 in 5 years at a certain rate of interest. If the true discount is $300, what is the present worth?
A.
$1200
B.
$1300
C.
$1400
D.
$1500
Show solution
Solution
True Discount = Amount - Present Worth. Present Worth = 1500 - 300 = $1200.
Correct Answer:
A
— $1200
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Q. A sum of money amounts to $1800 after 2 years at a certain rate of interest. If the true discount is $200, what is the present worth?
A.
$1600
B.
$1700
C.
$1800
D.
$1900
Show solution
Solution
Present Worth = Amount - True Discount. Thus, Present Worth = 1800 - 200 = $1600.
Correct Answer:
A
— $1600
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Q. A sum of money amounts to $5000 in 5 years at a rate of 4% per annum. What is the true discount?
A.
$300
B.
$400
C.
$500
D.
$600
Show solution
Solution
Present Worth = Amount / (1 + rt) = 5000 / (1 + 0.04*5) = 5000 / 1.20 = $4166.67. True Discount = 5000 - 4166.67 = $833.33.
Correct Answer:
B
— $400
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Q. A sum of money amounts to $8000 in 4 years at a rate of 8% per annum. What is the true discount?
A.
$600
B.
$700
C.
$800
D.
$900
Show solution
Solution
Present Worth = Amount / (1 + rt) = 8000 / (1 + 0.08*4) = 8000 / 1.32 = $6060.61. True Discount = 8000 - 6060.61 = $1939.39.
Correct Answer:
B
— $700
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Q. A sum of money is invested at 10% per annum for 4 years. If the true discount is $400, what is the sum?
A.
$4000
B.
$4400
C.
$4800
D.
$5200
Show solution
Solution
Let the sum be x. True Discount = x * Rate * Time / 100. 400 = x * 10 * 4 / 100. Solving gives x = $4000.
Correct Answer:
B
— $4400
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Q. A sum of money is invested at 15% per annum. If the true discount on it for 4 years is $240, what is the present worth?
A.
$1000
B.
$1200
C.
$1400
D.
$1600
Show solution
Solution
True Discount = Present Worth * Rate * Time / 100. Let Present Worth = x. Then, 240 = x * 15 * 4 / 100. Solving gives x = $1200.
Correct Answer:
B
— $1200
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Q. A sum of money is invested at 8% per annum. If the true discount on it for 2 years is $160, what is the present worth?
A.
$800
B.
$1000
C.
$1200
D.
$1400
Show solution
Solution
True Discount = Present Worth * Rate * Time / 100. Let Present Worth = x. Then, 160 = x * 8 * 2 / 100. Solving gives x = $1000.
Correct Answer:
B
— $1000
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Q. A sum of money is invested at a certain rate of interest for 4 years. If the true discount is $400, what is the present worth if the rate of interest is 5%?
A.
$1600
B.
$2000
C.
$2400
D.
$2800
Show solution
Solution
Let Present Worth = x. True Discount = x * Rate * Time / 100. 400 = x * 5 * 4 / 100. Solving gives x = $2000.
Correct Answer:
B
— $2000
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Q. A sum of money is invested at a rate of 6% per annum. If the true discount on the sum for 5 years is $500, what is the sum?
A.
$3000
B.
$3500
C.
$4000
D.
$4500
Show solution
Solution
Let the sum be x. True Discount = x * 6 * 5 / 100. Thus, 500 = x * 30 / 100. Solving gives x = $1666.67. Therefore, the sum = $1666.67 + $500 = $2166.67.
Correct Answer:
C
— $4000
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Q. A sum of money is invested at a rate of 8% per annum. If the true discount on the sum for 5 years is $400, what is the sum?
A.
$2000
B.
$2500
C.
$3000
D.
$3500
Show solution
Solution
Let the sum be x. True Discount = x * 8 * 5 / 100. Thus, 400 = x * 40 / 100. Solving gives x = $1000. Therefore, the sum = $1000 + $400 = $1400.
Correct Answer:
A
— $2000
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Q. If a sum of $3000 is due in 6 years at a rate of 9% per annum, what is the true discount?
A.
$200
B.
$300
C.
$400
D.
$500
Show solution
Solution
Present Worth = 3000 / (1 + 0.09*6) = 3000 / 1.54 = $1948.05. True Discount = 3000 - 1948.05 = $1051.95.
Correct Answer:
D
— $500
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Q. If the present worth of a sum is $2000 and the true discount is $400, what is the rate of interest per annum for 2 years?
A.
5%
B.
10%
C.
15%
D.
20%
Show solution
Solution
True Discount = Present Worth * Rate * Time / 100. 400 = 2000 * Rate * 2 / 100. Rate = (400 * 100) / (2000 * 2) = 10%.
Correct Answer:
B
— 10%
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Q. If the present worth of a sum is $600 and the true discount is $100, what is the amount after 2 years at 10% per annum?
A.
$700
B.
$800
C.
$900
D.
$1000
Show solution
Solution
Amount = Present Worth + True Discount = 600 + 100 = $700. Amount after 2 years = 700 * (1 + 0.10)^2 = $800.
Correct Answer:
C
— $900
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Q. If the present worth of a sum is $600 and the true discount is $150 for 3 years, what is the rate of interest?
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Solution
True Discount = Present Worth * Rate * Time / 100. Thus, 150 = 600 * r * 3 / 100. Solving gives r = 8%.
Correct Answer:
C
— 7%
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Q. If the present worth of a sum is $800 and the true discount is $200 for 2 years, what is the rate of interest?
A.
10%
B.
12.5%
C.
15%
D.
20%
Show solution
Solution
True Discount = Present Worth * Rate * Time / 100. Thus, 200 = 800 * r * 2 / 100. Solving gives r = 12.5%.
Correct Answer:
B
— 12.5%
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Q. If the true discount on a sum is $100 and the sum is due in 3 years at a rate of 15% per annum, what is the sum?
A.
$800
B.
$900
C.
$1000
D.
$1100
Show solution
Solution
Let the sum be x. True Discount = x * Rate * Time / 100. 100 = x * 15 * 3 / 100. Solving gives x = $800.
Correct Answer:
C
— $1000
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Q. If the true discount on a sum is $120 and the sum is due in 3 years at 6% interest, what is the sum?
A.
$2000
B.
$2200
C.
$2400
D.
$2600
Show solution
Solution
True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 120 = x * 6 / (100 + 6*3). Solving gives x = $2400.
Correct Answer:
C
— $2400
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