Determining Gross Amount from Net Amount

[kiwnjey]

Hello,

I have a basic question for you. Let's say I've received a net payment of 100 euros and need to calculate the gross amount to pay taxes to the tax authority, with a tax rate of 16% in my country.

I found a formula on the internet that suggests multiplying the net amount by 1 plus the VAT percentage (in my case, 1.16 since the VAT is 16%). This calculation results in a gross amount of 116 euros.

However, I'm having trouble verifying this calculation:

• If 116 euros represents 100%, 1% would be 1.16 euros.
• 16% would be 18.56 euros.
• Subtracting 18.56 euros from the gross amount of 116 euros leaves me with only 97.44 euros, less than the initial net payment of 100 euros.

Something seems amiss, and I'm unsure where I'm going wrong. Can you please provide some guidance?

 

[stapel]

I have a basic question for you. Let's say I've received a net payment of 100 euros and need to calculate the gross amount to pay taxes to the tax authority, with a tax rate of 16% in my country.

I found a formula on the internet that suggests multiplying the net amount by 1 plus the VAT percentage (in my case, 1.16 since the VAT is 16%). This calculation results in a gross amount of 116 euros.

However, I'm having trouble verifying this calculation:

• If 116 euros represents 100%, 1% would be 1.16 euros.
• 16% would be 18.56 euros.
• Subtracting 18.56 euros from the gross amount of 116 euros leaves me with only 97.44 euros, less than the initial net payment of 100 euros.

Something seems amiss, and I'm unsure where I'm going wrong. Can you please provide some guidance?

As you have proven, the proposed formula is not valid. (Thank you for showing your work and reasoning so nicely!)

You have some net amount "n". There is some gross amount "g". The tax percentage is 16% (or 0.16 as a decimal). The net amount is the gross amount, less 16% of the gross amount; in other words, the net amount is 84% of the gross amount. So use the standard percent-of set-up:

(this) is (some percentage) of (that)

Use this to create an equation.

You have the value for "n". Plug that in, divide through, and simplify to get your answer.

 

[kiwnjey]

Thank you for the help!

Regarding the calculation itself, your breakdown made it much clearer:

Net Amount (n) = Gross Amount (g) - Tax Percentage (16% or 0.16) * Gross Amount (g)

Solving for the gross amount (g):

g = n / (1 - Tax Percentage)

 

[scottbrandon]

Hello,

I have a basic question for you. Let's say I've received a net payment of 100 euros and need to calculate the gross amount to pay taxes to the tax authority, with a tax rate of 16% in my country.

I found a formula on the internet that suggests multiplying the net amount by 1 plus the VAT percentage (in my case, 1.16 since the VAT is 16%). This calculation results in a gross amount of 116 euros.

However, I'm having trouble verifying this calculation:

• If 116 euros represents 100%, 1% would be 1.16 euros.
• 16% would be 18.56 euros.
• Subtracting 18.56 euros from the gross amount of 116 euros leaves me with only 97.44 euros, less than the initial net payment of 100 euros.

Something seems amiss, and I'm unsure where I'm going wrong. Can you please provide some guidance?

Hello. The formula you found online is correct. To calculate the gross amount, you need to multiply the net amount by 1 plus the tax rate. So, for a net payment of 100 euros and a tax rate of 16%, the gross amount would indeed be 116 euros. Your calculation is accurate.