True Discount

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?

A. 4%
B. 5%
C. 6%
D. 7%

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?

A. 4%
B. 5%
C. 6%
D. 7%

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?

A. 5%
B. 6%
C. 7%
D. 8%

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

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

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?

A. 5%
B. 6%
C. 7%
D. 8%

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%

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

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?

A. 5%
B. 6%
C. 7%
D. 8%

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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%

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

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?

A. 5%
B. 6%
C. 7%
D. 8%

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%

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

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

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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True Discount

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