Simple Interest

2. At the end of the lesson, the
learner is able to compute
interest, maturity value, and
present value in simple interest
environment, and solve problems
involving simple interest.

3. 1.Compute simple interest
2.Compute maturity value
3.Compute unknown principal,
rate, or time

5. When invested at an annual interest
rate of 7%, the amount earned
P11,200 of simple interest in two
years. How much money was
originally invested?

6. When invested at an annual interest rate of 7%, the amount
earned P11,200 of simple interest in two years. How much
money was originally invested?
Given: r = 7% = 0.07 t = 2 years 𝑰𝒔 = 11,200
Find: Amount invested or principal P
𝑷 =
𝑰𝒔
𝒓𝒕
𝑷 =
𝟏𝟏, 𝟐𝟎𝟎
(𝟎. 𝟎𝟕)(𝟐)
𝑷 = 𝟖𝟎, 𝟎𝟎𝟎
Answer: The amount
invested is P 80,000.

7. If an entrepreneur applies for a loan
amounting to P500,000 in a bank,
the simple interest of which is P157,500
for 3 years, what interest rate is being
charged?

8. If an entrepreneur applies for a loan amounting to P500,000 in a
bank, the simple interest of which is P157,500 for 3 years, what
interest rate is being charged?
Given: P = 500,000 t = 3 years 𝑰𝒔 = 157,500
Find: interest rate (r)
r =
𝑰𝒔
𝑷𝒕
𝒓 =
𝟏𝟓𝟕, 𝟓𝟎𝟎
(𝟓𝟎𝟎, 𝟎𝟎𝟎)(𝟑)
r= 𝟎. 𝟏𝟎𝟓 = 𝟏𝟎. 𝟓%
Answer: The bank
charged an annual
simple interest rate of
10.5%.

9. How long will a principal
earn an interest equal to
half of it at 5% simple
interest?

10. How long will a principal earn an interest equal to
half of it at 5% simple interest?
Given: P r = 5% = 0.05 𝑰𝒔 =
𝟏
𝟐
P = 0.5P
Find: t
t =
𝑰𝒔
𝑷𝒓
𝒕 =
𝟎. 𝟓𝑷
(𝑷)(𝟎. 𝟎𝟓)
t = 𝟏𝟎 𝒚𝒆𝒂𝒓𝒔
Answer: It will take 10
years for a principal to
earn half of its value at 5%
simple annual interest rate.

14. Find the maturity value if 1 million
pesos is deposited in a bank at an
annual simple interest rate of 0.25%
after (a) 1 year (b) 5 years?

15. Find the maturity value if 1 million pesos is deposited in a
bank at an annual simple interest rate of 0.25% after
(a) 1 year (b) 5 years?
Given: P = 1,000,000 r = 0.25% = 0.0025
Find: (a) maturity or future value F after 1 year
(b) maturity or future value F after 5 years
Method 1
𝑰𝒔 = 𝑷𝒓𝒕
t = 1
𝑰𝒔 = (𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎)(𝟎. 𝟎𝟎𝟐𝟓)(𝟏)
𝑰𝒔 = 𝟐, 𝟓𝟎𝟎
Maturity Value
𝑭 = 𝑷 + 𝑰𝒔
𝑭 = 𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎 + 𝟐, 𝟓𝟎𝟎
𝑭 = 𝟏, 𝟎𝟎𝟐, 𝟓𝟎𝟎

16. Find the maturity value if 1 million pesos is deposited in a
bank at an annual simple interest rate of 0.25% after
(a) 1 year (b) 5 years?
Given: P = 1,000,000 r = 0.25% = 0.0025
Find: (a) maturity or future value F after 1 year
(b) maturity or future value F after 5 years
Method 2
To directly solve
the future value F,
t = 1
Maturity Value
𝑭 = 𝑷(𝟏 + 𝒓𝒕)
𝑭 = (𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎)(𝟏 + 𝟎. 𝟎𝟎𝟐𝟓 𝟏 )
𝑭 = 𝟏, 𝟎𝟎𝟐, 𝟓𝟎𝟎

17. Find the maturity value if 1 million pesos is deposited in a
bank at an annual simple interest rate of 0.25% after
(a) 1 year (b) 5 years?
Given: P = 1,000,000 r = 0.25% = 0.0025
Find: (a) maturity or future value F after 1 year
(b) maturity or future value F after 5 years
Method 1
𝑰𝒔 = 𝑷𝒓𝒕
t = 5
𝑰𝒔 = (𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎)(𝟎. 𝟎𝟎𝟐𝟓)(𝟓)
𝑰𝒔 = 𝟏𝟐, 𝟓𝟎𝟎
Maturity Value
𝑭 = 𝑷 + 𝑰𝒔
𝑭 = 𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎 + 𝟏𝟐, 𝟓𝟎𝟎
𝑭 = 𝟏, 𝟎𝟏𝟐, 𝟓𝟎𝟎

18. Find the maturity value if 1 million pesos is deposited in a
bank at an annual simple interest rate of 0.25% after
(a) 1 year (b) 5 years?
Given: P = 1,000,000 r = 0.25% = 0.0025
Find: (a) maturity or future value F after 1 year
(b) maturity or future value F after 5 years
Method 2
To directly solve
the future value F,
t = 5
Maturity Value
𝑭 = 𝑷(𝟏 + 𝒓𝒕)
𝑭 = (𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎)(𝟏 + 𝟎. 𝟎𝟎𝟐𝟓 𝟓 )
𝑭 = 𝟏, 𝟎𝟏𝟐, 𝟓𝟎𝟎

19. What are the amount of
interest and maturity value of
loan for P25,000 at 12%
simple interest for 5 years?

20. What are the amount of interest and maturity value of loan for
P25,000 at 12% simple interest for 5 years?
Given: P = 25,000 r = 12% = 0.12 t = 5 years
Find: (a) 𝑰𝒔
(b) F
𝑰𝒔 = 𝑷𝒓𝒕
𝑰𝒔 = (𝟐𝟓, 𝟎𝟎𝟎)(𝟎. 𝟏𝟐)(𝟓)
𝑰𝒔 = 𝟏𝟓, 𝟎𝟎𝟎
Maturity Value
𝑭 = 𝑷 + 𝑰𝒔
𝑭 = 𝟐𝟓, 𝟎𝟎𝟎 + 𝟏𝟓, 𝟎𝟎𝟎
𝑭 = 𝟒𝟎, 𝟎𝟎𝟎

21. How much money will you have
after 4 years and 3 months if
you deposited P10,000 in a
bank that pays 0.5% simple
interest?

22. How much money will you have after 4 years and 3 months if you
deposited P10,000 in a bank that pays 0.5% simple interest?
Given: P = 10,000 r = 0.5% = 0.005 t = 4.25 years
Find: F
𝑭 = 𝑷(𝟏 + 𝒓𝒕)
𝑭 = (𝟏𝟎, 𝟎𝟎𝟎)(𝟏 + 𝟎. 𝟎𝟎𝟓 𝟒. 𝟐𝟓 )
𝑭 = 𝟏𝟎, 𝟐𝟏𝟐. 𝟐𝟓

23. At what simple interest
rate per annum will P 1
become P 2 in 2 years?

24. At what simple interest rate per annum will P1 become P2 in
2 years?
Given: P = 1 F = 2 t = 2 years 𝑰𝒔 = 𝑭 − 𝑷 = 𝟐 − 𝟏 = 𝟏
Find: r
𝒓 =
𝑰𝒔
𝑷𝒕
𝒓 =
𝟏
(𝟏)(𝟐)
𝒓 = 𝟎. 𝟓
𝒓 = 𝟓𝟎%

25. How long will 1 million
pesos earn a simple interest
of 100,000 at 1% per
annum?

26. How long will 1 million pesos earn a simple interest
of 100,000 at 1% per annum?
Given: P = 1,000,000 𝑰𝒔 = 𝟏𝟎𝟎, 𝟎𝟎𝟎 r = 1% = 0.01
Find: t
𝒕 =
𝑰𝒔
𝑷𝒓
𝒕 =
𝟏𝟎𝟎, 𝟎𝟎𝟎
(𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎)(𝟎. 𝟎𝟏)
t = 𝟏𝟎 𝒚𝒆𝒂𝒓𝒔

27. How much should you
invest at the simple interest
is 7.5% in order to have
P300,000 in 2 years?

28. How much should you invest at the simple interest is
7.5% in order to have P300,000 in 2 years?
Given: r = 7.5% = 0.075 𝑭 = 𝟑𝟎𝟎, 𝟎𝟎𝟎 t = 2
Find: P
𝑷 =
𝑭
𝟏 + 𝒓𝒕
𝑷 =
𝟑𝟎𝟎, 𝟎𝟎𝟎
𝟏 + (𝟎. 𝟎𝟕𝟓)(𝟐)
P = 𝟐𝟔𝟎, 𝟖𝟔𝟗. 𝟓𝟕
𝑭 = 𝑷(𝟏 + 𝒓𝒕)

29. Complete the table by finding the unknown.
Present
Value
(P)
Rate
(r)
Time
(t)
Interest
(I)
Maturity
Value
(F)
8,000 8% 6 years (1) (2)
5,000 (3) 1 month (4) 6,000
(5) 12%
5 years
and 3
months
400,000

30. Solve the following problems.

31. 1. Find the simple interest on a loan of P65,000 if
the loan is given at a rate of 20% and is due in 3
years.
2. Amparo invested a certain amount at 10%
simple interest per year. After 2 years, the
interest she received amounted to P3,000. How
much did she invest?
3. Miko borrowed P25,000 at 10% annual simple
interest rate. How much should he pay after 3
years and 6 months?

32. 4. How long will an amount of money triple at
a simple interest rate of 1% per annum?
5. How long will an amount of P50,000 gain a
simple interest of P10,000 at 4% per annum?
6. At what simple interest rate will an amount
of money gain 50% of the principal in 4
years?
7. At what simple interest rate per annum will
P20,000 accumulate to P25,000 in 3 years?

33. 8. If you deposit P5,500 in a bank at an annual
simple interest rate of 0.5% , how much
money will you have after 12 years?
9. How much money should you deposit in a
bank so that it will accumulate to P100,000
at 1% simple annual interest for 10 years?
10.How much should you invest at 6% annual
interest rate to obtain a simple interest of
P72,000 in 3 years?