Banker’s Discount is a concept in finance related to bill discounting or the valuation of negotiable instruments before maturity. It is often calculated as the Simple Interest on the face value of a bill for the period from the date of discounting until the date of maturity. Banker’s Discount problems frequently appear in various competitive exams and are vital for understanding commercial transactions and financial instruments.

## 1. What is the Banker's Discount on a bill of $1000 due 1 year hence at 10% per annum?

a) $100

b) $110

c) $120

d) $130

### Answer:

a) $100

### Explanation:

```
- Banker's Discount = Simple Interest on Face Value
- BD = PRT / 100
- BD = 1000 * 10 * 1 / 100 = $100.
```

## 2. The Banker's Discount on a certain sum due 2 years hence is $180. The true discount is $160. Find the sum.

a) $900

b) $920

c) $1000

d) $1080

### Answer:

b) $920

### Explanation:

```
- BD - TD = SI on TD.
- 180 - 160 = SI on $160.
- Rate = (SI * 100) / (P * T) = (20 * 100) / (160 * 2) = 6.25%.
- Sum = TD / [(R * T) / 100] = 160 / [(6.25 * 2) / 100] = $920.
```

## 3. A bill of $600 is drawn on July 14 and is payable after 3 months. Find the banker's discount and the true discount if the rate is 8% per annum.

a) BD: $12, TD: $11.76

b) BD: $14, TD: $13.60

c) BD: $16, TD: $15.84

d) BD: $18, TD: $17.28

### Answer:

a) BD: $12, TD: $11.76

### Explanation:

```
- BD = (PRT) / 100 = (600 * 8 * 3/12) / 100 = $12.
- PV = 100 * BD / [100 + (R * T)] = 100 * 12 / [100 + (8 * 3/12)] = $588.24.
- TD = Face Value - PV = 600 - 588.24 = $11.76.
```

## 4. A bill for $2000 is drawn on May 15 and is discounted on July 20 at 5%. Find the Banker's Discount.

a) $15

b) $20

c) $25

d) $30

### Answer:

c) $25

### Explanation:

```
- Time from July 20 to maturity = 3 months minus 5 days.
- BD = (PRT) / 100 = (2000 * 5 * 85/365) / 100 = $25 (approx).
```

## 5. A 6-month bill of $3000 is discounted on Banker's discount at 10%. What is the true discount?

a) $150

b) $140

c) $130

d) $120

### Answer:

a) $150

### Explanation:

```
- BD = (PRT) / 100 = (3000 * 10 * 6/12) / 100 = $150.
- TD = BD / [1 + (RT/100)] = 150 / [1 + (10 * 6/12)/100] = $150.
```

## 6. The true discount on a bill due 9 months hence at 12% per annum is $540. Find the amount of the bill.

a) $2400

b) $2500

c) $2600

d) $2700

### Answer:

d) $2700

### Explanation:

```
- TD = (PW * R * T) / 100, where PW is the present worth.
- TD = $540, R = 12%, T = 9/12 years.
- PW = TD / [(R * T) / 100] = 540 / [(12 * 9/12) / 100] = $5400 / 9 = $600.
- Amount = PW + TD = $600 + $540 = $2700.
```

## 7. A bill for $500 is due after 8 months. What will be the banker's discount if the rate is 6% per annum?

a) $20

b) $24

c) $28

d) $30

### Answer:

b) $24

### Explanation:

```
- BD = (PRT) / 100 = (500 * 6 * 8/12) / 100 = $24.
```

## 8. A bill of $800 is drawn on April 15 and is payable after 4 months. Find the true discount and proceeds if discounted on June 19 at 5% per annum.

a) TD: $15, Proceeds: $785

b) TD: $20, Proceeds: $780

c) TD: $25, Proceeds: $775

d) TD: $30, Proceeds: $770

### Answer:

a) TD: $15, Proceeds: $785

### Explanation:

```
- Time from June 19 to maturity = 2 months minus 4 days.
- BD = (PRT) / 100 = (800 * 5 * 56/365) / 100 = $7.67 (approx).
- PV = 100 * BD / [100 + (R * T)] = 100 * 7.67 / [100 + (5 * 56/365)] = $762.95 (approx).
- TD = Face Value - PV = 800 - 762.95 = $37.05 (approx).
- Proceeds = Face Value - TD = 800 - 37.05 = $762.95 (approx).
```

## 9. If the banker's gain on a certain bill due 10 months hence at 12% per annum is $36, find the face value of the bill.

a) $1800

b) $2000

c) $2200

d) $2400

### Answer:

b) $2000

### Explanation:

```
- Banker's Gain (BG) = BD - TD.
- BG = SI on TD, where SI = PRT / 100.
- TD = BG / [(R * T) / 100] = 36 / [(12 * 10/12) / 100] = $360.
- BD = BG + TD = 36 + 360 = $396.
- Face Value = BD / [(R * T) / 100] = 396 / [(12 * 10/12) / 100] = $2000.
```

## 10. A bill is drawn for $1200 and is discounted at 5% per annum simple interest. If the banker's discount is $60, find the period for which the bill is drawn.

a) 6 months

b) 5 months

c) 4 months

d) 3 months

### Answer:

c) 4 months

### Explanation:

```
- BD = (PRT) / 100.
- $60 = (1200 * 5 * T/12) / 100.
- Solving for T, T = 4 months.
```

## 11. A bill is due 4 years hence. The creditor agrees to take a certain sum of money at present instead of the bill at a discount rate of 5%. If the sum is $1900, find the amount of the bill.

a) $2500

b) $2400

c) $2300

d) $2200

### Answer:

a) $2500

### Explanation:

```
- Present Worth (PW) = Amount / [1 + (R * T) / 100].
- $1900 = Amount / [1 + (5 * 4) / 100].
- Solving for the Amount, Amount = $1900 * [1 + (20/100)] = $2500.
```

## 12. The banker's discount on a sum of money for 1.5 years is $120, and the true discount is $100. Find the sum.

a) $800

b) $900

c) $1000

d) $1100

### Answer:

c) $1000

### Explanation:

```
- BD - TD = SI on TD.
- 120 - 100 = SI on $100.
- Rate = (SI * 100) / (P * T) = (20 * 100) / (100 * 1.5) = 13.33%.
- Sum = TD / [(R * T) / 100] = 100 / [(13.33 * 1.5) / 100] = $1000.
```

## 13. A bill of $1500 is discounted at a bank at 5%. The true discount is $120. Find the banker's discount.

a) $140

b) $130

c) $125

d) $115

### Answer:

b) $130

### Explanation:

```
- TD = (PW * R * T) / 100.
- $120 = (PW * 5 * T) / 100.
- PW = $1500 - $120 = $1380.
- BD = (1500 * 5 * T) / 100.
- Replacing T with its equivalent from the TD formula, BD = $130.
```

## 14. A bill for $1200 due 6 months hence is discounted at a bank at 6%. Find the amount of discount.

a) $36

b) $38

c) $40

d) $42

### Answer:

a) $36

### Explanation:

```
- BD = (PRT) / 100 = (1200 * 6 * 6/12) / 100 = $36.
```

## 15. The banker's gain on a bill due 2 years hence at 5% per annum is $50. Find the face value of the bill.

a) $1000

b) $1100

c) $1200

d) $1300

### Answer:

c) $1200

### Explanation:

```
- Banker's Gain (BG) = BD - TD = SI on TD.
- TD = BG / [(R * T) / 100] = 50 / [(5 * 2) / 100] = $500.
- BD = BG + TD = 50 + 500 = $550.
- Face Value = BD / [(R * T) / 100] = 550 / [(5 * 2) / 100] = $1200.
```