The document provides a comprehensive guide on calculating percentage increases, decreases, discounts, and simple interest. It includes formulas and multiple examples demonstrating how to find the percent of change for various scenarios. Additionally, it covers concepts related to commission rates and sales tax calculations.

1. PERCENTAGE

2. Imagine you’re at a store and see a sign that
says “25% off” or “30% more than before!”.
How would you calculate the actual discount
or increase in price?
That’s what we’ll learn today.

3. What is the Percent of Change?
The percent of change indicates how much
a quantity increases or decreases based on the
original amount.

4. a. Percentage Increase – The original value
increases by a certain percentage.
Here’s the formula we’ll use:
Percentage of Increase =
= x 100%

5. Example 1: The notebook price was originally Php
15.00 but it is now Php 21.00. How much did the
price increase?
Solution:
1. First, find the increase in value:
New amount – Original amount 21-15 = 6
2. Then, use the formula:
6 / 15 x 100 = 40%
Therefore, the notebook price increased by 40% from its
original price

6. Example 2: A certain brand of a smart phone increased
from 10,000.00 in January to 15,000.00 in June due
₱ ₱
to its more upgrade version. What is the percentage
increase in the amount of smart phone?
Solution:
1. First, find the amount increase:
New amount – Original amount
= 15,000 – 10,000 = 5,000
2. Then, use the formula: =
Therefore, the smart phone
price increased by 50%
from its original price

7. Example 3: Boyet’s weight at start of December is 50kg.
Pinoy celebrates Christmas season by eating and fun
with friends for the whole month, so at the end of
December Boyet’s weight rise to 65 kg. What is the
percentage increase in his weight?
Solution:
1. First, find the amount increase:
New weight – Original weight = 65 – 50 = 15
2. Then, use the formula: =
Therefore, Boyet’s weight
increased by 30% from his
original weight.

8. b. Percentage Decrease – The original value
decreases by a certain percentage.
Here’s the formula we’ll use:
Percentage of decrease =
= x 100%

9. Example 1: Suppose a bag originally cost
₱200.00, but now it’s on sale for ₱180.00. What’s
the percentage decrease?
Solution:
1. First, find the decrease in value:
Original amount - New amount = 200-180 = 20
2. Then, use the formula:
20 / 200 x 100 = 10%
So, the bag decreased by 10% from its original cost.

10. Example 2: Makoy’s weight is 70kg, after diet and
exercise for two months his weight is 55 kg. What
is the percentage decrease in his weight?
Example 3: What rate of discount is given if a
lady’s blouse that regularly for 80 is sold for
₱
60?
₱
Sol: PD =
PD = = 21%
PD = = 25%

11. Example 4: John paid 16,000 for a laptop after
₱
receiving a 20% discount. What was the original
price of the item assuming that no sales tax was
added?
Sol: Original Value=
OV=
=

12. Example 5: Today there are 45 present students in
Grade 7 math class. This number of present
students is decreased by 10%. How many students
should there be yesterday?
Sol: OV=
OV=
=

13. Exercises 1: A phone originally cost ₱ 5,000.00
but is now selling for ₱ 4,200.00. What’s the
percentage decrease?
Exercises 2: If your allowance increased from
₱100.00 to ₱150.00, what’s the percentage
increase?
16%
50%
Exercises 3: Lauren bought a car for ₱622,500.00.
If she received a 17% discount, what was the
original price of the vehicle?
₱750,000

14. Have you ever wondered how to calculate
discounts when shopping, determine the commission
earned by a salesperson or determine the total
cost of an item, including sales tax?

15. A discount is a reduction in the original price. The
percent (%) discount is the discount rate.
Formula:
Discount = Original price x discount rate
Example 1: If a shirt originally costs ₱450.00 and
there’s a 25% discount:
Discounted = ₱ 450 x .25 = ₱ 112.50
New Price of shirt: ₱ 450 - ₱ 112.50 = 337.50
₱

16. Given:
₱400 = original price
Example 2: The original price or marked price of
a book is 400. How much is the discount and sale
₱
price if 20% discount rate is given to the first 10
costumers?
20%= discount rate
Discount= ?
Sale price = ?
Discount= (original)(discount rate)
Discount = (400)(20%)
= (400)(0.20)
= ₱ 80.00
₱ 80.00

17. Given:
₱400 = original price
Example 2: The original price or marked price of
a book is 400. How much is the discount and sale
₱
price if 20% discount rate is given to the first 10
costumers?
20%= discount rate
Discount= ?
Sale price = ?
Sale price: Original price - discount
Sale price = 400 - 80
₱ ₱
= ₱ 320.00
₱ 80.00
₱ 320.00

18. Given:
₱500 = sale price
Example 3: Find the original price or marked
price of a T-shirt that is sold for 500 at 20%
₱
reduction.
20%= discount rate
Original price =
Original price =
original price =
= ₱ 625.00
=
= ₱ 625.00

19. Given:
₱800 = original price
Example 4: What rate of discount is given if a
men’s bag that regularly 800 is sold for
₱
700.00?
₱
₱700=sale price
Discount rate =
Discount rate =
Discount rate: 12.5%
Discount
₱800 – 700 =
₱ ₱ 100
= 0.125(100%)

20. Given:
₱24,000 = original price
Example 5: If Haley paid 14,400 for a
₱
discounted laptop and the original price is
24,000.00, what was the discount rate?
₱
₱14,400=sale price
Discount rate =
Discount rate =
Discount rate: 40%
Discount
₱24,000 – 14,400
₱
= ₱ 9,600
= 0.4(100%)

21. A commission is a percentage of a sale price given
to a salesperson as payment. The percent (%) of
commission is the commission rate.
Example 1: If a salesperson earns a 7%
commission on a Php 200,000 sale:
Commission = Php 200,000 x 0.07 = Php 14,000
Commission = Total sales x commission rate

22. Example 2: Venus is a realtor. She receives 3%
commission when she sells a lot. How much
commission will she receive for selling a lot that
costs 850,000.00?
₱
Given:
₱850,000.00=Total sales
3% = commission rate
Commission -?
Commission = (total sales)(commission rate)
=( 850,000)(3%)
₱
commission= 25,500.00
₱
=( 850,000)(0.03)
₱

23. Example 3: Makkoy earned 520.00 commission
₱
when she sold a 13,000.00 bicycle. What rate of
₱
commission did he get?
Given:
₱520=commission
₱ 13,000=total sales
Commission rate -?
Commission rate =
¿
₱ 520
₱ 13,000
(100 %)
Commission rate=4%
0.04 (100%)

24. Example 4: Macky earned 800.00 as commission
₱
for total sales of school supplies he sold. How much
is the total sales if this is 5% of school supplies he
sold?
Given:
₱800=commission
5%=commission rate
Total sales=?
Total sales =
¿
₱ 800
5%
Total sales = 16,000.00
₱
¿
₱ 800
0.05

25. Sales tax is a
percentage added to
the sale price of an
item. To calculate the
total cost, including
sales tax, we use the
formula:
Total cost = Original
price + sales tax
Sales tax = (Original price x Sales Tax Rate)

26. Example 1: If an item costs Php 500.00 and the
sales tax rate is 8%:
Total cost = Original price + sales tax
= 500 + (500 x 0.08)
= 500 + 40
= Php 540.00

27. Example 2: A group of students ate in a fast food
restaurant. If their orders totals 750.00 plus a
₱
12% VAT, how much is the total amount they paid
to the cashier?
Total cost = 750 + (750 x 0.12)
= 750 + 90 = ₱840.00
The total amount they paid is ₱840.00

28. Example 3: Manny bought a bicycle in a super
market (SM), where the sales tax rate was 12% of
the purchase price. What was the sales tax of a
bicycle if the purchase price was 15,000.00
₱ How
about total cost or total amount of a bicycle?
Total cost = 15,000 + (15000 x 0.12)
= 15,000 + 1,800 = ₱16800.00
The sales tax of a bicycle is 1,800
₱
The total amount of a bicycle is ₱16,800.00

29. Example 4: Madel bought a new smartphone for
8,000.00 plus sales tax. She was surprised when
₱
she got the receipt and saw that the tax was
880.00. What was the sales tax rate for this
₱
purchase?
Tax rate =
=
Tax rate = 11%
= 0.11 (100%)

30. Example 5: The sales tax rate of a t-shirt is 10%.
How much is the purchased price of the t-shirt if
the sales tax is 50.00.
₱
Purchase price =
=
Purchase price = 500.00
= 500.00

31. Example 6: Diego bought a new bag for
1,600.00. He was surprised that the seller then
₱
added 128.00. What was the sales tax rate for
₱
this purchase?
Sales tax =

32. Simple interest is a percentage added to the sale
price of an item. To calculate the total cost,
including sales tax, we use the formula:
Total cost = Original price +
(Original price x Sales Tax Rate)
Example: If an item costs Php 500.00 and the
sales tax rate is 8%:
Total cost = 500 + (500 x 0.08)
= 500 + 40 = Php 540.00

33. Simple Interest
Interest – the amount earned from investing or
borrowing money
Interest rate – the percent of interest
Principal – the amount of money invested or
borrowed
Time – the length of time the money was invested
or the length of time the borrowed money will be
paid (in years)

34. Simple Interest
Principal Rate Time Interest
₱100 8% p.a. 1 year ₱8
₱100 8% p.a. 2 years ₱16
₱100 8% p.a. 3 years ₱24
₱100 8% p.a. 4 years ₱32

35. Simple Interest

36. Example 1. Mackoy borrowed 30,000 at 10%
₱
annual simple interest rate. How much is the
interest for 3 years?
Given:
P = 30,000
₱
r = 10% or 0.10
t = 3
I = ?
I = Prt
I = ( 30,000 )(0.10)(3)
₱
I = 9,000
₱
Interest for 3 years = 9,000
₱

37. Example 2. Mike received 10,000
₱ loan from
bank. After 2 years, he paid back 11,200 and
₱
closed the loan. Find the rate of interest.
Given:
P = 11,200
₱
r = ?
t = 2
I = 1,200
₱
r = Interest rate = 6%
r =
r =
r = 0.06 (100) = 6%

38. Example 3. How much money must be invested at
15% interest annually to earn 500.00 monthly?
₱
Given:
P = ?
r = 15%
t = 1
I = 6,000
₱
P =
Money invested= 40,000
P =
P =
P = 40,000

39. Example 4. If a loan is taken out for 15,500.00
₱
at 11% interest rate and cost 5,115.00, how
₱
long was the loan for?
Given:
P = 15,500.00
₱
r = 11%
t = ?
I = 5,115.00
₱
t =
Loan term is 3 years
t =
t =
t = 3 years