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Percentage Increase
Percentage increase measures how much a value has increased relative to its original amount.
In basic terms, how much did it go up by?
This is used in multiple areas such as:
- Salary increases
- Tuition fee increases
- Price increases
- Population growth
Fun fact: 60-75% of the tuition fee increases goes into the salary increase of a teacher.
Formula
Percentage Increase = (New Value - Original Value) / Original Value · 100%
Percentage Decrease
Percentage decrase measures how much a value has decreased compared to its original amount.
In basic terms, how much did it go down by?
This is used in multiple areas such as:
- Depreciation
- Price reduction
- Population decline
- Budget cuts
Formula
Percentage Decrease = | (New Value - Original Value) / Original Value | · 100%
Which basically has no difference to the other one, except there is an absolute value for negative values to be converted to positive ones.
Inflation
Inflation is the continuous increase in the general prices of goods and services over time.
In basic terms, how much did it go up by overtime?
This is used in multiple areas such as:
- Food prices
- Fuel prices
- Transportation fares
- Tuition fees
Formula
New Price = Original Price · (1 + Inflation Rate)
Apparently in January, inflation rate was up to 7.5%. Inflation rate would make normally 20,000 worth of groceries into 21,500. Today on July 31, it's 6.4% - still unbelievably high as it's supposed to sit at 2-4%
Mark-Up & Mark-Down
These two are basically the same thing in the opposite direction. Mark-up is the amount added to the cost price to determine the selling price - which is what makes up for the cost, while Mark-down is the reduction from the original selling price - or looking for the original price from the benefit-induced one.
“Part ng negosyo ay malugi, kahit paano.”
The failures of capitalism right in that former term. I love me some capitalism.
This is what our professor says about multiple things - such as the electric bill from Meralco and books from OLFU.
SP (MU) = Cost · (1 + Mark-up Rate)
New Selling Price (MD) = Cost · (1- Mark-down Rate)
Discount
A discount is a reduction from the marked price.
Discount = Original Price x Discount Rate
Sale/Discounted Price = Original Price - Discount
Combined/Expanded:
Sale Price = Orig. Price - (Orig. Price(1 - DR))
For multiple discounts, where you just multiply the rates together:
Sale Price = Orig. Price(1-DR1)(1-DR2)(1-DR3)...
Value Added Tax (VAT)
VAT is a consumption tax added to the selling price of goods and services.
- In the Philippines, the standard VAT rate is 12%. Which is ironically, or unironically, the highest of Southeast Asia.
“Si VATMan ay si Ralph Recto (who increased VATs from 10% → 12%).”
Formula
VAT = Selling Price x 0.12
VAT Inclusive Price = Selling Price + VAT
Profit & Loss
Profit occurs when Selling Price > Cost Price. Loss occurs when Selling Price < Cost Price
Formula
Profit = Selling Price - Cost
Loss = Cost - Selling Price
These formulas rely solely on subtraction and do not require any mental gymnastics for most cases.
Examples
Percentage Decrease
Example 1
A notebook costs 40 pesos last year. This year it costs 50 pesos. Find the percentage increase.
PI = 10/40 x 100% = 25%
Example 2
A teacher’s monthly salary increased from 28,000 pesos to 31,500 pesos. Find the PI.
PI = 3500/28000 x 100% = 12.5%
Example 3
A motorcycle worth 95,000 pesos increased by 18%. Find the new selling price.
This time we must solve it by multiplying the original number by this formula:
Selling Point/New Price = cost(1 + rate)
Applying it:
NP = 95000(1+0.18) = 1.18(95000) = 112,100 Pesos
With the difference being 17,100 Pesos.
Examples
Example 1
A shirt costs 800 pesos. It is now 680 pesos. Find the percentage decrease.
PI = -120/800 x 100% = 15%
Example 2
A television costs 25,000. The price decreased by 12%. Find the new price.
Selling Point/New Price = cost(1 - rate)
Applying it:
NP = 25000(1-0.18) = .82(25000) = 22000 Pesos
With the difference being 17,100 Pesos.
Example 3
Enrollment dropped from 2,400 to 2040 students. Find the percentage decrease.
That's 15%. 360 students in decrease.
Inflation
Example 1
Rice costs 50 pesos/kg. Inflation is 8%. Find the new price.
NP = 50 x (1 + 0.08) = 54 Pesos
Inflation value of 4 pesos.
Example 2
Electricity bill is 2,800 pesos. Inflation is 6%. Find the new bill.
NP = 2800 x (1.06) = 2,968 Pesos
Inflation value of 168 pesos.
Example 3
A family’s monthly grocery budget is 12,500 pesos. Inflation is 9%. Find the additional amount and new budget.
NP = 12500 (1.09) = 13,625 Pesos
Inflated budget with 1,125 pesos.
Mark-Up & Mark-Down
Example 1
The cost is 500 pesos and the Mark-up rate is 20%. What’s the selling price?
SP = 500(1+.2) = 600 Pesos
Example 2
The original price is 1,800 pesos. With a Mark-down of 15%. What is the Mark-down price?
NSP = 1800(1-.15) = 1,530 Pesos.
Example 3
A store bought a printer for 8,500 pesos. It added a 35% mark-up, then offered a 10% mark-down. Find the final selling price.
There are two steps to this.
SP = 8500(1.35) = 11,475
NSP = 114,75(.9) = 10,327.50 Pesos
Discount
Example 1
The shoes worth 2,500 was discounted at 10%. What is the sale price?
Discount = Original Price x DR
Discount = 2500 x .10 = 250
Sale Price = Original Price - Discount = 2250
Example 2
A refrigerator costs 28,000 pesos. It has a 20% discount, then an additional 5% promotional discount on the discounted price. Find the final selling price.
SP = 28000 - 28000(0.8)(0.05) = 26880
VAT
Example 1
The products price is worth 500 pesos. Find the VAT and its inclusive price.
VAT = 500 x 0.12 = 60 pesos
VAT Incl. = 500 + 60 = 560
Example 2
The restaurant bill is worth 2,850 pesos. Find the VAT inclusive amount.
VAT = 2850 x 0.12 = 342
VAT Incl. = 3,192 pesos
Example 3
A furniture set costs 38,500 before VAT. Find its VAT and its VAT inclusive price.
VAT = 38500 x 0.12 = 4,620
VAT Incl. = 38500 + 4620 = 43,120 pesos
Profit & Loss
Example 1
The cost of a product is 400 pesos and its selling price is 520. How much is the profit?
Profit = 520 - 400 = 120 pesos
Example 2
The cost of a product is 18,000 pesos and its selling price is worth 16,500. How much is its loss?
Loss = 18000 - 16500 = 1,500 pesos.
Example 3
A bicycle costs 12,500 pesos. The owner marks it up by 25%, then gives a 10% discount. Determine the final selling price and the profit.
Mark-up price SP = 15,625
Discounted SP (Final) = 14062.50 Pesos
Profit = 14062.5-12500 = 1562.50 Pesos
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