Simple interest is interest earned on a principal amount for a specified period of time at a given interest rate. It is calculated by multiplying the principal, interest rate, and time. There are two types of simple interest calculations - ordinary interest which uses a 360 day year, and exact interest which uses a 365 day year. Examples are provided to demonstrate calculating simple interest using different principal amounts, interest rates, and time periods in days, months, or years. Calculating interest requires determining whether to use the exact time period or approximate it based on 30 day months for ordinary interest.

1. SIMPLE INTEREST

2. Simple Interest
- amount earned for one year
calculated by multiplying the principal
by the interest rate
- directly proportional to the principal,
interest rate and the term

3. FORMULA:
Interest = Principal x Interest rate x Time
Is = P r t
Is = simple interest
P = Principal amount, or the amount
invested or borrowed
r = interest rate
t = time of invest/ time of loan expressed
in years or fractional part of a year

4. Example
An amount of ₱ 7,300 𝑖𝑠 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑
for 3 years at a simple interest of
12% per annum.
Find the interest and the maturity
value.

5. Solution:
Given: P= ₱7,300 r= 12 % or 0.12 t= 3 years
Formula: Is = Prt
A. Interest
Is =Prt
Is =₱7,300(0.12)(3)
Is =₱2,628
The principal will earn an interest of ₱2,628.00

6. B. Maturity value or the Amount(A)
Formula: A= P + I
Solution: A=P+I
A= ₱ 7,300 + ₱ 2,628
A= ₱9,928
The maturity value is ₱ 9,928.00

7. Example
An investment of ₱ 10,000 is
transacted for 5 months at 6 %.
Find the interest and the
maturity value.

8. Solution:
Given:P=₱10,000 r=6%=0.06 t=5 mos.=
5
12
yr.
Formula: Is = Prt
A. Interest
Is =Prt
Is =₱10,000(0.06)(
5
12
)
Is =₱250
The principal will earn an interest of ₱250.00

9. B. Maturity Value
Formula: A= P + I
Solution: A=P+I
A= ₱ 10,000 + ₱ 250
A= ₱10,250
The maturity value is ₱ 10,250.00

10. Activity
An amount of ₱ 50,000 is invested in a
financial institution.
A. What is the interest if the principal reach
₱51,000?
B.How long will it take for the amount to reach
₱ 51,000 at 2% simple interest?
C. At what interest rate will it earn ₱ 1,000 in 10
months?
₱ 1000.00
1 year
2.4 %

11. Solution:
Given:
P= ₱ 50,000 A= ₱ 51,000
A. Is = A-P
Is = ₱51,000 -₱50,000
Is = ₱1000
The interest is ₱ 1000.00

12. B. From I = Prt, then t=
𝐼
𝑃𝑟
P= ₱ 50,000 r= 2% = 0.02 I=₱1000
t=
𝐼
𝑃𝑟
t=
₱1000
(₱50000)(0.02)
t= 1
It will take 1 year or 12 months for
₱50000.00 to reach ₱ 51000.00 at 2%
simple interest.

13. C. Given:
P=₱50000 I= ₱1000 t=10 mos.=
10
12
=
5
6
year
Solution: From I=Prt, then
r=
𝐼
𝑃𝑡
r=
₱ 1000
(₱50000)(
5
6
)
r=0.024
r=2.4 %

14. Activity
Page 255 / 271 #s 1-3

15. INTEREST AND TERMS
(Simple interest)

16. * define ordinary interest ,ordinary time, exact
interest and exact time;
* determine the ordinary and exact interest, and
* compute for the ordinary interest using exact
time, ordinary interest using ordinary time,
exact interest using exact time, and
exact interest using ordinary time.

17. TYPES OF SIMPLE INTEREST
1. ORDINARY INTEREST
2. EXACT INTEREST

18. Ordinary interest
*When interest is computed with denominator of
360.
Note: If the unknown in the problem is not stated, it
is implied to solve for the ordinary interest.

19. Ordinary Interest
-interest is computed based on a 360 days
in a year
-Banker’s Rule
Formulas:
Time: t =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑜𝑓 𝑎 𝑙𝑜𝑎𝑛
360
Ordinary interest: Io = (P)(r)
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒂𝒚𝒔
𝟑𝟔𝟎

20. Exact interest
*When interest is computed with
denominator of 365.

21. Exact Interest
-interest is computed in a 365 days in a
year as the time factor denominator
Formulas:
Time: t =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑜𝑓 𝑎 𝑙𝑜𝑎𝑛
365
Exact interest: Ie = (P)(r)
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒂𝒚𝒔
𝟑𝟔𝟓

22. FORMULAS:
When the time is expressed in number of days,
there are two ways of solve of solving the interests:
Simple Interest: Is = P r t
1. Ordinary interest: Io = P r t
Io = (P)(r)
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒂𝒚𝒔
𝟑𝟔𝟎
2. Exact interest: Ie = P r t
Ie = (P)(r)
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒂𝒚𝒔
𝟑𝟔𝟓

23. Find the ordinary and exact interest on a ₱ 25,750 loan at 5% interest rate at the
end of 45 days.
A. Ordinary Interest:
Given: P = 25,750 r = 5% = 0 .05 t =
45
360
Io = Prt
Io = (P)(r)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠
360
Io = (₱ 25,750) (0.05)
45
360
Io = (₱ 25,750) (0.05) 0.125
Io = ₱ 160.94
B. Exact Interest:
Given: P = 25,750 r = 5% = 0 .05 t =
45
365
Ie = Prt
Ie = (P)(r)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠
365
Ie = (₱ 25,750) (0.05)
45
365
Ie = (₱ 25,750)(0.05) 0.123288
Ie = ₱ 158.73
Answer: The ordinary interest of the loan is ₱ 160.94 while the exact interest of the loan is ₱ 158.73

24. Find the exact interest and the ordinary interest given
the following values: ₱10,000 for 100 days at 6%.
A. Exact Interest
Given:P=₱10,000 r=6%=0.06 t=
100
365
Ie = Prt
Ie = (P)(r)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠
365
Ie = ₱10,000(0.06)(
100
365
)
Ie = ₱ 164.38
B. Ordinary Interest
Given:P=₱10,000 r=6%=0.06 t=
100
360
Io = Prt
Io = (P)(r)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠
360
Io = ₱10,000(0.06)(
100
360
)
Io = ₱ 166.67
The exact interest is ₱ 164.38 while the ordinary interest is ₱ 166.67.

25. TYPES OF TERMS:
1. ORDINARY TIME
2. EXACT TIME

26. ORDINARY /APPROXIMATE TIME
-Based on 30-day month computation
-means that a 6-month transaction covers
(6)(30 days)=180 days

27. EXACT TIME
-based on exact number of inclusive dates of
transaction
-example: A loan entered on October 1, 2022 and
matured on December 20, 2022.
Oct. 2,2022 – Oct. 31,2022 30 days
Nov. 1,2022 – Nov.30,2022 30 days
Dec. 1,2022 – Dec. 20,2022 20 days
TOTAL 80 days

28. Problem
Find the interest on ₱28,700 at 7.3 %
from May 14,2022 to October 16,2022
using the following:
A. ordinary interest using exact time
B. ordinary interest using ordinary time
C. exact interest using exact time
D. exact interest using ordinary time

29. Tabulation of the exact time and ordinary time
(From May 14,2022 to October 16,2022)

30. Solutions:
A. Ordinary interest using Exact time
Given: P= ₱28,700 r= 7.3%=0.073 t=
155
360
Ioe = P r t
Ioe = (P)(r)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠
360
Ioe = ₱28,700(0.073)(
155
360
)
Ioe = ₱902.06

31. B. Ordinary interest using Ordinary/Approx. time
Given: P= ₱28,700 r= 7.3%=0.073 t=
152
360
Ioa = P r t
Ioa = (P)(r)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠
360
Ioa =₱28,700(0.073)(
152
360
)
Ioa = ₱884.60

32. C. Exact interest using Exact time
Given: P= ₱28,700 r= 7.3%=0.073 t=
155
365
Iee = P r t
Iee =(P)(r)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠
365
Iee =₱28,700(0.073)(
155
365
)
Iee = ₱889.70

33. D. Exact interest using Ordinary/Approx. time
Given: P= ₱28,700 r= 7.3%=0.073 t=
152
365
Iea =Prt
Iea =(P)(r)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠
365
Iea =₱28,700(0.073)(
152
365
)
Iea = ₱872.48

34. Answers:
A. The ordinary interest using exact time is ₱902.06.
B. The ordinary interest using ordinary time is ₱884.60.
C. The exact interest using exact time is ₱889.70.
D. The exact interest using ordinary time is ₱872.48.

35. Activity
Page 267 #s 1-2

36. Knuckle Counting Months
Count knuckles as 31 days,
depressions
between knuckles as 30
(or 28/29) days.
Start with the index
finger knuckle as January,
and count one finger or
depression at a time towards
the little finger knuckle (July),
saying the months while doing
so.