This document provides information on simple and compound interest, including definitions of key terms like principal, interest rate, and time period. It gives the formulas for calculating simple interest, compound interest, and maturity values. Several examples are worked out, such as calculating the interest earned on a bank deposit over 6 months, 1 year, and 18 months at a 2.75% interest rate. The document also contains practice problems for students to work through involving simple and compound interest concepts.
2. Lesson 1: Simple Interest
Simple Interest ( 𝑰𝒔) – interest that is computed on the
principal. The interest remains constant throughout the
term.
Lender or creditor – person (or institution) who invests
the money or makes the funds available.
Borrower or debtor – person (or institution) who owes
the money or avails of the funds from the lender
3. Origin or loan date – date on which money is received by the
borrower
Repayment date or maturity date – date on which the money
borrowed or loan is to be completely repaid
Time or term (t) – amount of time in years the money is borrowed or
invested; length of time between the origin and maturity dates
Principal (P) – amount of money borrowed or invested on the origin
date
Rate(r) – annual rate, usually in percent, charged by the lender, or
rate of increase of the investment
Interest (I) – amount paid or earned for the use of money
Maturity value or future value (F) –amount after t years that the
lender receives from the borrower on the maturity date.
4. 𝐼𝑠 = 𝑃𝑟𝑡
where:
𝐼𝑠= Simple Interest
P = Principal or amount
invested or borrowed
r = simple interest rate
t = term of time in years
5. Example:
A working student in one of the biggest fast-food
restaurants in Lucena City wants to save for the upcoming
school year. He wants to deposit his money into 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.
6.
7. Problem Solving: 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.
Since she doesn’t have money on 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.
8.
9. Solve the following problems.
1. A couple with three children are peacefully living in a barangay
near the City proper. The husband is a government employee
while the wife is a rug sewer. They always remind their children
about this: “Bilhin and kailangan at huwag kailanganin ang hindi
kayang bilhin”. Because of this teaching, the children open a joint
account to a certain cooperative to have a better investment. The
total amount they earned in selling rugs, was put in their account in
the cooperative to help their parents. Their total earnings
amounting to ₱ 5,000.00 will earn an interest rate of . 7.5% per
year. Help them to compute for the simple interest earned and
maturity value, if their money will be invested in 3 years.
10. Lesson 2: Compound Interest
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.
11. 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
12. Problem Solving: 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. Since she doesn’t have
money on hand, she decided to borrow from a bank with a
start-up capital of ₱50,000.00 at 7% interest rate
compounded annually and payable within 5 years.
Compute for the interest yield.
13. Activity:
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.
21. Activity 1.1
1. If P = ₱4,500, r = 1.25% and t = 5 years, find the simple
interest.
a. What formula will be used? _______________________
b. How are you going to express the rate in decimal? _______
c. How much is the simple interest? ______________________
2. If P = ₱5,000, = 2% and t = 8 mos., find the maturity
value.
a. Which formula will you use? __________________________
b. How are you going to express the time in years?_________
c. How much is the maturity value?_______________
22.
23. Lesson 4: Interest, Maturity, Future, and Present
Values in Compound Interest
24.
25. Example 1: Given: P= ₱18,500, r = 3% and compounded
annually for 3 years, find the maturity value (F) and the
compound interest (𝐼𝐶).
26. Example 2: Given F = ₱15,000, r = 2% compounded
annually for 4 years, find the present value (P).
27. Compounding More Than Once a Year
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 (𝒊𝒎
) - annual rate of interest or interest rate
per year
Rate (j) of interest for each conversion period
𝑗 =
𝑖𝑚
𝑚
=
𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛
28.
29. The formula of Maturity Value for interest compounding
m times a year is:
30.
31.
32. Read each statement and answer the question that follows.
1. If P = ₱85,500, and r = 1.25% compounded monthly for
1 year, find the compound interest.
2. If F = ₱50,000 with the rate 1.5% compounded quarterly
for 5 years find the present value and compound interest
3. Find the compound interest and maturity value if P =
₱43,000, with a rate of 5% is compounded semi-annually
for 6 years.
4. Find the compound interest and present value if F =
₱105,000 with a rate of 2.5% is compounded quarterly for
3 years
33. Answer the following simple interest
problems.
1. Mariel deposited ₱ 16,000.00 in a bank
that offers a simple interest rate of 1.75%.
If she placed the money for 7 years, how
much interest will she earn?
2. Janice has a loan with an interest rate
of 1.5%. The amount of interest is ₱
2,250.00 for a period of 3 years. How
much is her loan?
34. 3. How much did Josie invest if the maturity value is
₱38,500.00 and the simple interest computed is at 1.12%
for 6 years?
4. Jamie invested a certain amount of money in JDJ Savings
Bank with a 2.5% interest rate. He received ₱ 2,250.00 as
interest after 2 years from his investment. How much did
he invest?
5. Marinel received ₱ 1,450,500.00 as her inheritance from
her parents. She deposited the said amount in a time
deposit with 1% interest rate per annum, how much
money will be accumulated after 7 years?
35. Answer the following compound interest problems.
1. Jasmin borrowed money from a bank at the rate of
1.89% compounded semi – annually. If the amount she
borrowed is ₱ 13,000.00, how much interest will she need
to pay at the end of 6 years?
2. Arthur wants to set aside an amount to be invested in a
fund earning 1.02% compounded quarterly, if he wants to
accumulate ₱ 250,000.00 in 4 years, how much must he set
aside?
3. How much must Michelle set aside and invest in a fund
earning 2.1% compounded quarterly if she wants to
accumulate ₱ 50,000.00 in 5 years?
36. 4. How much should be deposited in a bank paying
1.15% compounded semi – annually to accumulate an
amount of ₱ 80,000.00 in 5 years?
5. James invested ₱150,000.00 at 2.5% interest
compounded semi – annually. Find the maturity value
if he invests for (a) 4 years? (b) 8 years? (c) How
much is the additional interest earned due to the
longer time?
