Working with Percentages

You know the saying: “use it or lose it”, don’t you?  Well, I am no different. Years ago when I focused on back-office management accounting, I was constantly 10-keying all sorts of numbers up and down, in and out, into and out of sheets, systems and tools (yeah, I loved it). What drives me up the wall today, each and every time is when I am stumped with a simple question working with percentages – so this blog will serve as my “cheat sheet” I will refer to going forward and I hope it’s helpful for others too.

Since I am from / live in Germany, I will use a comma instead of a decimal as do the majority of countries, when separating between €uros and €uro Cents.  Access “Countries Using a Comma” for further details.  We’ll also be using value added tax (VAT) in some of our calculations.  Calculator entries are highlighted in red.  So, let’s begin!

Calculate the net from the gross price of €uro 148,20 and the gross from the net (19% VAT)

  • 148,20 / 1,19 = 124,5378 (€uro 124,54)
  • 124,54 * 1,19 = 148,2026 (€uro 148,20)

Calculate the net from the gross price of €uro 148,20 and the gross from the net (7% VAT)

  • 148,20 / 1,07 = 138,5046 (€uro 138,50)
  • 138,50 * 1,07 = 148,195 (€uro 148,20)

Calculate 19% and 7% VAT from the gross price of €uro 148,20

  • 148,20 / 119 * 19 = €uro 23,66
  • 148,20 / 107 * 7 = €uro 9,70

Calculate 19% VAT to add on top of the net price of €uro 124,54

  • 124,54 * 0,19 = €uro 23,66

Calculate 7% VAT to add on top of the net price of €uro 138,50

  • 138,50 * 0,07 = €uro 9,70

You sell your professional services for €uro 120 per hour plus 19% VAT

  • 120 + (19% of 120) = 120 + (0,19 x 120) = €uro 142,80
  • 120 * (100% + 19%) = 120 * (1,00 + 0,19) – OR – 120 * 1,19 = €uro 142,80

You quote your total, hourly price of €uro 142,80 to the client including 19% VAT (gross); how does one calculate the price before VAT?

  • The gross amount (100% + 19%) = 119% or 1,19 – divide the gross amount of €uro 142,80 / by 1,19 which equals your net amount of €uro 120,00 (142,80 / 1,19 = 120)

You need to change percentages into decimals in order to work with them for other calculations?

  • 45% (45 / 100 = 0,45)
  • 7% (7 / 100 = 0,07)

You need to change decimals to percentages?

  • 0,45 * 100 = 45%
  • 0,07 * 100 = 7%

You need to convert fractions to percentages; changing fractions to decimals?

  • 4/5 = 0,80 = 80% (4 / 5 *100 = 80%)
  • 3/4 = 0,75 = 75% (3 / 4 * 100 = 75%)

Within your family of two parents and eight children, each have their own nicknames – you were responsible for designing nine of those nicknames.  What percent of those nine were created by you?

  • 13 = 100%
  • 9 = 69% (9 / 13 = 0,6923)

Your gross pay per month during the year of 1991 was 2.346,80 – your gross pay per month during the year of 1992 was 3.608,29; what percentage increase / change did you experience from 1991 to 1992?

  • Calculate the difference between the two amounts (3608,29 – 2346,80 = 1261,49)
  • Make a fraction of the difference over the first of the two amounts (1261,49 / 2346,80 = 0,5375)
  • Convert the fraction to a percentage by dividing the denominator into 100 times the numerator (126149 / 2346,80 = 53,75%)
  • Your gross salary increase from 1991 to 1992 equals 53,75%

As a real-estate agent, you mediate the sale of a small condominium for €uro 92.000,00 and collect commission (including 19% VAT) of 5,95% – calculate the gross and net commission and clarify the 5,95% commission to your buyer.

  • Gross commission the buyer pays you = €uro 5.474,00 (92000 * 0,0595 = 5474)
  • Your net commission = €uro 4.600,00 (5474 / 1,19 = 4600)
  • 92000 * 0,05 = €uro 4.600,00 (your net commission)
  • 92000 * 0,0095 = €uro 874,00 (the 19% VAT you collect from the buyer and submit to your local tax authorities)
  • Your explanation to the buyer for the 5,95% gross commission is that you expect 5% net commission from the selling price of €uro 92.000,00 and the additional 0,95% includes the 19% VAT required for each percentage point of commission (5 * 0,19 = 0,95%)

Your real-estate agent requires 5,95% commission if your object is sold through his rendered services and 2,38% if you rent an apartment or house from him; why 5,95% and 2,38%?  What do these percentages mean?

  • Sale with 5,95% commission – 5% = the net commission with 19% VAT on top (0,19 * 5 = 0,95)
  • Rental with 2,38% commission – 2% = the net commission with 19% VAT on top (0,19 * 2 = 0,38)
  • The real-estate agent includes 19% VAT (that he submits to his local tax authorities) in the total percentage of commission provided – like the gross amount you would note or rather pay on any other purchase of goods and services (excluding food and books)

As a real-estate agent, you work for a franchise-based real-estate broker.  The franchise requires the broker to pay 9% for all transactions of its agents and the broker requires you to give 20% of your commission to the brokerage, leaving you with 80% of the end-brokerage commission.  How do you calculate your gross commission that you end-up banking for a rental apartment you mediated for €uro 625,00 monthly rent (w/o utilities) if the regulated commission from your region is 2 times monthly rent?  How do you calculate the overall percentage of commission you would end-up receiving from the initial transaction?  For this calculation, focus on net commission only, without local VAT.

  • Monthly rent w/o utilities €uro 625,00 * 2 = €uro 1.250,00 less 9% franchise fee of 112,50 (1250 / 100 * 9 = 112,50) = €uro 1.137,50
  • From the brokerage commission of €uro 1.137,50 you bank 80% (1137,50 * 0,80 = 910,00), leaving 20% (1137,50 * 0,20 = 227,50) for your broker
  • Considering your banked amount of €uro 910,00, you take home ca. 73% of the original commission (910 / 1250 = 0,728)

Working with Percentages

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