# VAT: Recalculate Gross Amount (With Tax Included), 60, From 15.5% Original VAT Rate to the New Rate of 8%. Calculate the Net Amount (Without Tax), the New Price (Gross Amount) and the Value of the VAT Tax

## Calculate the Gross Amount 60 with a different VAT Rate

### Gross Amount = The amount with VAT included (including VAT)

### Net Amount = The amount without VAT (excluding VAT)

### 1. Rewrite the Gross Amount.

#### Formula:

#### Original VAT Amount = Original VAT Rate × Net Amount

#### Gross Amount = Net Amount + Original VAT Amount

#### ⇒ Substitute for the Original VAT Amount in the Gross Amount formula

#### Gross Amount =

#### Net Amount + Original VAT Amount =

#### Net Amount + (Original VAT Rate × Net Amount) =

#### Net Amount × (1 + Original VAT Rate)

### 2. Calculate the Net Amount:

#### Formula:

#### Gross Amount = Net Amount × (1 + Original VAT Rate)

#### ⇒ Net Amount = Gross Amount ÷ (1 + Original VAT Rate)

#### Calculation:

#### Net Amount =

#### 60 ÷ (1 + 15.5%) =

#### 60 ÷ (1 + ^{15.5}/_{100}) =

#### 60 ÷ (1 + 15.5 ÷ 100) =

#### 60 ÷ (1 + 0.155) =

#### 60 ÷ 1.155 ≈

#### 51.948051948052 ≈

#### 51.95

(Rounded off to a maximum of 2 decimals)

### 3. Calculate the VAT Amount due to the Original VAT Rate:

#### Formula:

#### Original VAT Amount =

#### Gross Amount - Net Amount

#### Calculation:

#### Original VAT Amount =

#### 60 - 51.948051948052 =

#### 8.051948051948 ≈

#### 8.05

(Rounded off to a maximum of 2 decimals)

### 4. Calculate the VAT Amount due to the New VAT Rate:

#### Formula:

#### New VAT Amount =

#### New VAT Rate × Net Amount

#### Calculation:

#### New VAT Amount =

#### 8% × 51.948051948052 =

^{8}/_{100} × 51.948051948052 =

#### 8 ÷ 100 × 51.948051948052 =

#### 8 × 51.948051948052 ÷ 100 =

#### 415.584415584416 ÷ 100 ≈

#### 4.155844155844 ≈

#### 4.16

(Rounded off to a maximum of 2 decimals)

### 5. Calculate the New Gross Amount.

#### Formula:

#### New Gross Amount =

#### Net Amount + New VAT Amount

#### Calculation:

#### New Gross Amount =

#### 51.948051948052 + 4.155844155844 =

#### 56.103896103896 ≈

#### 56.1

(Rounded off to a maximum of 2 decimals)

## Net Amount = 51.95

Original VAT Amount (15.5%) = 8.05

New VAT Amount (8%) = 4.16

New Gross Amount = 56.1 (- 3.9 vs. initial)

#### Used symbols: % percent, ÷ divide, × multiply, = equal, / fraction bar, ≈ approximately equal;

#### Writing numbers: comma ',' as thousands separator; point '.' as a decimal mark.

### More operations, calculate prices with new VAT Rates:

## Recalculate Gross Amount (Tax Included) with a New VAT Rate

#### Gross Amount = Net Value × (1 + Tax%)

#### Net Amount = Gross Amount ÷ (1 + Tax%)

## The Latest Gross Amounts Recalculated With New VAT Rates

## Calculate the Gross Amount (With Tax Included) With Different, New, VAT Rates

### Step 1: Calculate the Net Amount (Without Tax)

- Initial Gross Amount = Net Amount + Initial Tax Amount
- Initial Tax Amount = Initial Tax% × Net Amount
- Initial Gross Amount = Net Amount + Initial Tax% × Net Amount = (1 + Initial Tax%) × Net Amount
#### Initial Gross Amount = (1 + Initial Tax%) × Net Amount

In conclusion: #### Net Amount = Initial Gross Amount ÷ (1 + Initial Tax%) =

### Step 2: Add the New Tax Amount to the Net Amount

- New Gross Amount = Net Amount + New Tax Amount
- New Tax Amount = New Tax% × Net Amount
- New Gross Amount = Net Amount + New Tax% × Net Amount = (1 + New Tax%) × Net Amount
- In conclusion, New Gross Amount = (1 + New Tax%) × Net Amount = (1 + New Tax%) × Initial Gross Amount ÷ (1 + Initial Tax%) =
^{(1 + New Tax%)}/_{(1 + Initial Tax%)} × Initial Gross Amount #### New Gross Amount = ^{(1 + New Tax%)}/_{(1 + Initial Tax%)} × Initial Gross Amount

### Examples of calculations:

**Case 1: Initial Tax Rate = 20%, New Tax Rate = 19% **

Step 1, Calculate Net Amount:

(1 + Initial Tax%) = 1 + 20% = ^{100}/_{100 + 20/100 = 120/100 = 1.2 => Initial Gross Amount = 1.2 × Net Amount, and Net Amount = Initial Gross Amount ÷ 1.2 Step 2, Add the New Tax Amount: New Gross Amount = (1 + New Tax%) × Net Amount = (1 + 19%) × Net Amount = (100/100 + 19/100) × Net Amount = 119/100 × Net Amount = 1.19 × Net Amount = 1.19 × Initial Gross Amount ÷ 1.2 = 1.19/1.2 × Initial Gross Amount Answer: New Gross Amount = (1.19 ÷ 1.2) × Initial Gross Amount}**Case 2: Initial Tax Rate = 20%, New Tax Rate = 5% **

Step 1, Calculate Net Amount:

(1 + Initial Tax%) = 1 + 20% = ^{100}/_{100} + ^{20}/_{100} = ^{120}/_{100} = 1.2 => **Initial Gross Amount** = 1.2 × Net Amount, and **Net Amount** = Initial Gross Amount ÷ 1.2

Step 2, Add the New Tax Amount:

**New Gross Amount** = (1 + New Tax%) × Net Amount = (1 + 5%) × Net Amount = (^{100}/_{100} + ^{5}/_{100}) × Net Amount = ^{105}/_{100} × Net Amount = 1.05 × Net Amount = 1.05 × Initial Gross Amount ÷ 1.2 = ^{1.05}/_{1.2} × Initial Gross Amount

Answer: **New Gross Amount** = (1.05 ÷ 1.2) × Initial Gross Amount.