Discounting Bills of Exchange

1. Find the True Discount on ₹1,040 due 8 months hence at 6% p.a.

Correct Answer: A) ₹40

Step 1: Identify variables. Bill Value (B.V.) = ₹1,040, Rate (R) = 6%, Time (T) = 8 months = 8/12 years = 2/3 years.

Step 2: Use the True Discount formula: TD = (B.V. × R × T) / (100 + (R × T))

Step 3: Calculate R × T = 6 × (2/3) = 4

Step 4: TD = (1040 × 4) / (100 + 4) = 4160 / 104 = ₹40

2. Find the Banker’s Discount on ₹6,080 due 4 months hence at 4% p.a.

Correct Answer: B) ₹81.06

Step 1: Identify variables. B.V. = ₹6,080, R = 4%, T = 4 months = 4/12 years = 1/3 years.

Step 2: Use the Banker’s Discount formula: BD = (B.V. × R × T) / 100

Step 3: BD = (6080 × 4 × (1/3)) / 100

Step 4: BD = 6080 × 4 / 300 = 24320 / 300 = 81.066…

Step 5: Rounding to two decimal places gives ₹81.06

3. Find the True Discount on the present value: ₹10,000, payable after 3 months at 10% p.a.

Correct Answer: A) ₹250

Step 1: Identify variables. Present Value (P.V.) = ₹10,000, R = 10%, T = 3 months = 3/12 years = 1/4 years.

Step 2: When Present Value is given, True Discount is the Simple Interest on the Present Value: TD = (P.V. × R × T) / 100

Step 3: TD = (10000 × 10 × (1/4)) / 100

Step 4: TD = 10000 × 2.5 / 100 = ₹250

4. Find the Banker’s Discount when the Bill Value is ₹1,040 and True Discount is ₹40.

Correct Answer: B) ₹41.60

Step 1: Identify variables. B.V. = ₹1,040, True Discount (TD) = ₹40.

Step 2: Find Present Value (P.V.) = B.V. – TD = 1040 – 40 = ₹1,000.

Step 3: The relationship is: BD = (B.V. × TD) / P.V. OR BD = (B.V. × TD) / (B.V. – TD)

Step 4: BD = (1040 × 40) / 1000 = 41600 / 1000 = ₹41.60

5. Find the True Discount on ₹1,380 due 1.5 years hence at 10% p.a.

Correct Answer: C) ₹180

Step 1: Identify variables. B.V. = ₹1,380, R = 10%, T = 1.5 years.

Step 2: Use formula: TD = (B.V. × R × T) / (100 + (R × T))

Step 3: Calculate R × T = 10 × 1.5 = 15

Step 4: TD = (1380 × 15) / (100 + 15) = 20700 / 115 = ₹180

6. Find the Banker’s Discount on ₹5,400 due 8 months hence at 12% p.a.

Correct Answer: B) ₹432

Step 1: Identify variables. B.V. = ₹5,400, R = 12%, T = 8 months = 8/12 years = 2/3 years.

Step 2: Use Banker’s Discount formula: BD = (B.V. × R × T) / 100

Step 3: BD = (5400 × 12 × (2/3)) / 100

Step 4: BD = 5400 × 8 / 100 = 43200 / 100 = ₹432

MCQ Test: True Discount & Banker’s Discount