Which formula correctly computes withholding tax?

Which formula correctly computes withholding tax?

• A. (net amount received / (100 - tax rate deducted)) x tax rate
• B. net amount received x tax rate / 100
• C. tax rate x 100 / net amount received
• D. (net amount received - tax rate) x 100

Answer: (A)

When tax is withheld, the tax amount must be such that the gross payment (before tax) equals the net amount received plus the tax itself. If you know the net amount received and the tax rate, you can back out the tax by using the relationship between gross and net. Let the net amount be what the recipient gets after tax, and the tax rate be the percentage of the gross that is withheld. The gross amount before tax is net divided by (1 minus the tax rate in decimal form). If tax rate is given as a percentage, that becomes net divided by (100 − tax rate) and then multiplied by the tax rate to get the tax withheld. In formula form, tax withheld = net × tax rate / (100 − tax rate). This is algebraically the same as net ÷ (100 − tax rate) × tax rate. For example, if net received is 70 and the tax rate is 30%, the tax withheld is 70 ÷ 70 × 30 = 30, which makes the gross amount 100 (70 + 30). The other options don’t produce the correct relationship: one would apply the rate directly to the net, which ignores that tax is taken from the gross; another mixes up the order of operations; and the last option combines the net and rate in a way that yields an unpacked, nonsensical result.

When tax is withheld, the tax amount must be such that the gross payment (before tax) equals the net amount received plus the tax itself. If you know the net amount received and the tax rate, you can back out the tax by using the relationship between gross and net.

Let the net amount be what the recipient gets after tax, and the tax rate be the percentage of the gross that is withheld. The gross amount before tax is net divided by (1 minus the tax rate in decimal form). If tax rate is given as a percentage, that becomes net divided by (100 − tax rate) and then multiplied by the tax rate to get the tax withheld. In formula form, tax withheld = net × tax rate / (100 − tax rate). This is algebraically the same as net ÷ (100 − tax rate) × tax rate.

For example, if net received is 70 and the tax rate is 30%, the tax withheld is 70 ÷ 70 × 30 = 30, which makes the gross amount 100 (70 + 30).

The other options don’t produce the correct relationship: one would apply the rate directly to the net, which ignores that tax is taken from the gross; another mixes up the order of operations; and the last option combines the net and rate in a way that yields an unpacked, nonsensical result.