VAT: Recalculate Gross Amount (With Tax Included), 161.5, From 19% Original VAT Rate to the New Rate of 13%. Calculate the Net Amount (Without Tax), the New Price (Gross Amount) and the Value of the VAT Tax

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

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

Gross Amount = Net Value × (1 + Tax%)

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

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/<sub>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</sub>
• 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.