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 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 $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 $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 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 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. 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 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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Q. If the true discount on a sum is $150 and the sum is due in 1 year at 5% interest, what is the sum?

A. $3000
B. $2500
C. $2000
D. $1500

Solution

True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 150 = x * 5 / (100 + 5). Solving gives x = $2500.

Correct Answer: B — $2500

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Q. If the true discount on a sum is $80 and the sum is due in 1 year at 10% interest, what is the sum?

A. $800
B. $900
C. $1000
D. $1100

Solution

True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 80 = x * 10 / (100 + 10). Solving gives x = $1000.

Correct Answer: C — $1000

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Q. 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?

A. 15%
B. 20%
C. 25%
D. 30%

Solution

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

Correct Answer: A — 15%

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Q. If the true discount on a sum of money is $200 and the rate of interest is 10% per annum for 2 years, what is the present worth?

A. $800
B. $1000
C. $1200
D. $1500

Solution

True Discount = Present Worth * Rate * Time / 100. Let Present Worth = x. Then, 200 = x * 10 * 2 / 100. Solving gives x = $1000.

Correct Answer: B — $1000

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Q. If the true discount on a sum of money is $250 and the present worth is $1250, what is the time period at 8% per annum?

A. 1 year
B. 2 years
C. 3 years
D. 4 years

Solution

True Discount = Present Worth * Rate * Time / 100. 250 = 1250 * 8 * Time / 100. Time = (250 * 100) / (1250 * 8) = 2 years.

Correct Answer: B — 2 years

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Q. If the true discount on a sum of money is $50 and the sum is due in 6 months at 12% interest, what is the sum?

A. $500
B. $600
C. $700
D. $800

Solution

True Discount = Sum * Rate / (100 + Rate). Let Sum = x. Then, 50 = x * 12 / (100 + 12/2). Solving gives x = $600.

Correct Answer: B — $600

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True Discount

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