This document discusses simple and compound interest. Simple interest is calculated on the principal only, while compound interest is calculated on the principal and accumulated interest over time. The key formulas for simple interest are presented, along with examples of calculating simple interest for scenarios like deposits, loans, and investments. Compound interest is explained as interest earned on both the principal and past interest. Formulas and examples are provided for calculating compound interest accrued over time at different compounding periods.

1. SIMPLE INTEREST

2. NAME ME ACTIVITY
•It is interest that is computed on the principal.
The interest remains constant throughout the
term.
•A person (or institution) who invests the money
or makes the funds available
•A person (or institution) who owes the money or
avails of the funds from the lender
•It is the date on which money is received by the
borrower

3. •It is date on which the money
borrowed or loan is to be completely
repaid.
•It is the amount of time in years the
money is borrowed or invested; length
of time between the origin and
maturity dates
•It is the amount of money borrowed or
invested on the origin date

4. •It is the annual rate, usually in percent,
charged by the lender, or rate of increase
of the investment
•It is the amount paid or earned for the use
of money
•It is the amount after t years that the
lender receives from the borrower on the
maturity date

5. SIMPLE INTEREST FORMULA
I = Prt
•where:
Is= Simple Interest
P= Principal or amount invested or borrowed
r= simple interest rate
t= term of time in years

6. The formula can be manipulated to obtain
the following relationships:
•The formula for finding the principal
amount
𝑃=
Is
𝑟𝑡
•The formula for finding the rate
r =
Is
𝑃𝑡

7. • The formula for finding the time
t =
Is
𝑃𝑟
• To find the maturity (future) value, you can use either of the
following:
𝐹=𝑃 (1+𝑟𝑡) or 𝐹=𝑃 + 𝐼𝑠
where:
F = maturity (future) value
Is = simple interest
P = principal or the amount invested or borrowed or present value
r = simple interest rate
t = time or term in years

8. Ordinary and Exact Simple Interest
•In ordinary simple interest, the interest is
computed on the basis of one banker’s year.
1 banker’s year= 12 months = 300 days
•In exact simple interest, the interest is based
on the exact number of days of the year,
where there are 365 days for an ordinary
year and 366 days for leap years.

9. LET’S PRACTICE
1. A working student at one of the biggest fast-
food restaurants in Lucena City wants to save for
the upcoming school year. He wants to deposit
his money to a Filipino owned bank so that even
in a simple way he can help his fellow Filipino.
Supposed his monthly salary is ₱10,000.00, and
it was deposited to an account that earns a
simple interest of 2.75% per annum. Find the
simple interest after 6 months, one year, and 18
months.

10. 2. Due to COVID-19 pandemic Miss Dada a
female resident of Brgy. May Pagkakaisa
somewhere in Quezon Province thinks of a
business that can provide for her needs as well
as the need of her neighbors so she can be of
help even in this trying time.
Having no money at hand she decided to borrow
from a bank as the start-up capital of
₱50,000.00 at 7% simple interest rate payable
within 5 years. Compute for the interest yield.

11. 3. Find the interest on 6800.00 for 3 years at 11% simple
interest.
4. What is the principal amount if the amount of interest at the
end of 2
1
2
year is P4,500 for a simple interest of 6% per annum?
5. If P16,000 earns P480 in 9 months, what is annual rate of
interest?

12. 6. Given: 𝑃=₱18,500, 𝑟=0.03, 𝑡=5. Find simple
interest (𝐼𝑠)
7. Given: 𝑃=₱20,000, 𝐼𝑠=₱4,000, 𝑡=4 . Find the
rate (𝑟)
8. Given: 𝑃=₱40,000., 𝐼𝑠= ₱700, 𝑟=7%. Find
time (𝑡).
9. Given: 𝑃=₱15,000, 𝑡= 4 months, 𝑟=2%. Find
maturity (future) value (𝐹).
10. If P = ₱5,000, r = 2% and t = 8 mos.,
find the maturity value.

13. COMPOUND
INTEREST

14. Compound interest (𝑰𝒄) is the
interest computed on the principal
and also on the accumulated past
interest, so compound interest is a
way to earn money because you
don’t just earn using your original
money, but also the interest you
earned.
𝑰𝒄 = F – P

15. •If you are a debtor compound interest is
not good for you. Better yet pay your debt
in full the soonest possible so that the
burden of interest will not be on your
shoulder.
•Conversely, if you are an investor,
compound interest is your best buddy and
it is better to invest in a long period of
time for you to have a greater return of
your investment through interest earned.

16. •To demonstrate this, consider an investment of
P1000 to earn 10% per year for three years. The
following diagram shows how the money grows.
P1000
P1100 P1210 P1331

17. EXAMPLE
1. Due to COVID-19 pandemic Miss Dada a
female resident of Barangay May Pagkakaisa
somewhere in Quezon Province thinks of a
business that can provide for her needs as well
as the need of her neighbors so she can be of
help even in this trying time.
Having no money at hand she decided to
borrow from a bank as the start-up capital of
₱50,000.00 at 7% interest rate compounded
annually and payable within 5 years. Compute
for the interest yield.

18. EXAMPLE

19. EXAMPLE

20. EXAMPLE

21. 2. Assuming that your father asks you about investment and
wants to know the interest that will be earned if he will invest
₱500,000.00 in a certain bank that offers an annual
compounding interest of 8% for 5 years.

22. •Notice that the formula to find the future value in a
compound interest is given by
F = P(1+r)t
where:
𝐹 = future value
𝑃 = principal amount
𝑟 = compound interest rate
𝑡 = time or time in years.
• Also, to find the compound interest just deduct the
principal (P) from the computed future value (F).

23. 3. Given that F = ₱60,000 and P = ₱45,000 how
much is the compound interest?

24. 4. Accumulate P5,000 for
10 years at 8%
compounded annually.

25. QUIZ #2
Direction. Provide the following answers.
A. Supposed that a local farmer wants to
borrow money from Landbank of the
Philippines to start the organic farming in
his one (1) hectare of agricultural land. The
farmer needs ₱150,000.00 as start-up
capital. The bank offers him 10% interest
rate compounded annually. Compute for the
total amount to be paid every year for 5
years. Show your answer in tabular form.

26. P150,000 10%
P181,500
10%
10%
10%
10%
P16,500
P199,650
Complete the table below and provide solutions for each of the unknown.
P219,615
1. 2. 3.
4. 5. 6.
7. 8.
9. 10. 11. 12.
13. 14. 15.

27. 16. 17.
18. 19.
3 years 20.
B. Complete the table below and provide solutions for each of
the unknown.

30. Example 1: Given: P= ₱18,500, r = 3% and
compounded annually for 3 years, find the
maturity value (F) and the compound interest
(Ic ).
Example 2: Given F = ₱15,000, r = 2%
compounded annually for 4 years, find the
present value (P).

31. Compounding More Than Once a Year
In the examples above the interest
are compounded annually, however,
there are cases that interest is
compounded more than once a year so
in this case additional terms must be
clarified such as:

32. •The interval of time between successive
conversions of interest into principal is called
the interest period or conversion period
•It is usually either three months, six months or
one year, in which cases interest is said to be
compounded quarterly, semiannually, or
annually respectively. The total amount due at
any time is called the compound amount.
•

33. Frequency of Conversion(m) – number of conversion period in
one year
Conversion or interest period – time between successive
conversions of interest
Total number of conversion periods(n)
n = mt = (frequency of conversion) x (time in years)
Nominal rate (𝑖(𝑚)
) – annual rate of interest
Rate(j) of interest for each conversion period
j =
𝑖(𝑚)
𝑚
=
𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛

37. Example 3. Given 𝑃 = ₱50,000.00, 𝑖4
= 0.03, 𝑚
= 4, 𝑡 = 4, find F and Ic .
Example 4. Given = ₱45,000.00, 𝑖2
= 0.02, 𝑚 =
2, 𝑡 = 4, find Ic .

38. 5. Find the compound interest and maturity value
if P = ₱43,000, with a rate of 5% is compounded
semi-annually for 6 years.
6. Find the compound interest and present value
if F = ₱105,000 with a rate of 2.5% is
compounded quarterly for 3 years.