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Gen Math 11 Q2 Mod2 Interest-Maturity-Present-and-Future-Values-in-Simple-and-Compound-Interest Version 2-from-CE1-ce2-1
Accountancy (BSA2)
Quezon City University
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General Mathematics
Quarter 2 – Module 2:
Interest, Maturity, Future, and
Present Values in Simple and
Compound Interests
General Mathematics Alternative Delivery Mode Quarter 2 – Module 2: Interest, Maturity, Future, and Present Values in Simple First Edition, 2020
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On your previous module, you have already illustrated and distinguished the difference between simple and compound interests. A deeper analysis of this topic will be the focus of this module wherein the relationships among the variables in solving the simple and compound interest will be explored.
You will realize the importance of deriving a certain formula to compute the required variable involved in interest. The connection among interest, principal or present value, rate, time and maturity value will be reiterated. This topic will also revolve around money and since it is talking about money you will learn more on how to make decisions that concerns about it.
Are you now ready for the new lesson, if so you may proceed to this module and have fun while learning.
The module is composed of two lessons, namely:
Lesson 1 – Interest, Maturity, Future, and Present Values in Simple Interest Lesson 2 – Interest, Maturity, Future, and Present Values in Compound Interest
After going through this module, you are expected to:
- compute interest, maturity value, future value, and present value in simple interest environment;
- compute interest, maturity value. future value, and present value in compound interest environment; and
- derive the formula of simple and compound interest to compute the maturity, future, and present value.
What I Need to Know
Let’s find out how far you might already know about this topic by answering the assessment below. Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.
Which of the following is the formula to find the simple interest? a. 𝐼𝑠 = 𝑃𝑟𝑡 b. 𝐼𝑠 = 𝑃(1 + 𝑟)𝑡 c. 𝐼𝑠 = 𝐹 − 𝑃 d. 𝐼𝑠 = (1+𝑟)𝐹 𝑡
What formula will be used to find the present value of simple interest? a. 𝑃 = 𝐼𝑠𝑟𝑡 b. 𝑃 = 𝑟𝑡𝐼𝑠 c. 𝑃 = 𝑟𝑡𝐼 𝑠 d. 𝑃 = 𝐼𝑠𝑡𝑟
If the investment amounting to ₱35,000 earned an interest of ₱2,500 how much will be the maturity value? a. ₱32, b. ₱37, c. ₱30, d. ₱40,
Given that P = ₱5,250, r = 1% and t = 5 years, find the simple interest. a. ₱32,812. b. ₱3,281. c. ₱328. d. ₱32.
Given that P = ₱10,500, r = 4 12 % and t = 8 months, find the simple interest.
a. ₱ 315 b. ₱3, c. ₱3, d. ₱31,
What I Know
- If the maturity value is ₱23,000 and the compound interest is ₱3,500, how much is the present value? a. ₱26, b. ₱23, c. ₱19, d. ₱15,
For numbers 14 – 15, use the following values: P = ₱15,000, 𝑖 12 = 5%, t = 4 years, m = 12.
How much is the maturity value? a. ₱18, 313. b. ₱17, 413. c. ₱16, 313. d. ₱15, 413.
How much is the compound interest? a. ₱413. b. ₱1,313. c. ₱2,413. d. ₱3, 313.
Lesson
1
Interest, Maturity, Future,
and Present Values in
Simple Interest
Business transactions are common events we experienced in our daily lives. Some of these transactions are banking activities like withdrawal, deposits, and loans and some are done in supermarkets when customers used credit cards and others do it in the pawnshops. When these transactions occur there are two parties involved the lender and the borrower hence there involves a particular amount which we call interest.
Everything that we have right now is just borrowed, our talents, jobs, and even our lives. God is the sole persona who does not charge interest from what He lent. However, the money that we borrowed from others has a certain computation in finding the interest which will be tackled in this module.
For you to begin considering the previous lesson which is essential in obtaining success in this module. In the last module, you determine the difference between simple and compound interest. Simple interest pertains to the interest computed on the principal while compound interest is computed on the principal and also on the accumulated past interests.
Different terms related to simple and compound interest were also given emphasis such as the lender or creditor which refers to the person who invests or makes funds available and the borrower and debtor which refers to the person who owes the money.
Moreover, different terms essential in the interest formula were also explained such as time or term, principal or present value, rate, and maturity value. However, additional terms for compound interest were also given importance such as frequency of conversion, nominal rate, and rate of interest for each conversion period. These terms will be useful for you to have a better grasp of this module.
Other skills such as expressing percent to decimals is also necessary for example:
Express the following as decimal:
1. 12% - 0.
2. 10% - 0.
3. 300% - 3
4. 8 12 % - 0.
What’s In
Notes to the Teacher
Use of calculator in this module is allowed because it will help them to easily compute what is asked, however reiterate to the learners that to ensure the accuracy and precision of the solution the use of correct formula is necessary. Also, inform them that in other books different variables were used to represent the components of interest formula, it will not affect the result as long as the relationship with other variables is the same with the relationship to be presented in this module.
- Do you think it is wrong for Jamaica to buy a new cellphone?
- What can you say about Janice’s attitude towards money?
- How much will Janice save after two years?
- How do you value education?
From the previous conversation, you can say that one of the sources of funds of ordinary students is their allowance. A person always can decide on things they wanted to do on the money that they possess. In the scenario, you saw two different kinds of students. One who saves to be able to buy the things she wanted and the other one is saving for her future. In doing so she invested her money in a bank that earns interest. In computing the simple interest and other related components, the formula is
where:
Is = simple interest P = principal or the amount invested or borrowed or present value r = simple interest rate t = time or term in years
The formula can be manipulated to obtain the following relationships:
The formula for finding the principal amount
The formula for finding the rate
The formula for finding the time
What is It
####### 𝐼𝑠 = 𝑃𝑟𝑡
####### 𝑃 = 𝐼 𝑟𝑡𝑠
####### 𝑟 = 𝐼𝑠
####### 𝑃𝑡
####### 𝑡 = 𝐼𝑠
####### 𝑃𝑟
To find the maturity (future) value, you can use either of the following:
or
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
Let us take the following for example:
Example 1: Given: 𝑃 = ₱18, 500, 𝑟 = 0, 𝑡 = 5. Find simple interest (𝐼𝑠)
Solution: Use the formula of Simple Interest 𝐼𝑠 = 𝑃𝑟𝑡
Substitute the given to the formula 𝐼𝑠 = 18,500(0)(5)
Performing the operation 𝐼𝑠 = ₱2,
Therefore, the simple interest is ₱2,
Example 2: Given: 𝑃 = ₱20,000, 𝐼𝑠 = ₱4,000, 𝑡 = 4. Find the rate (𝑟)
Solution:
Use the formula in finding the rate 𝑟 = 𝑃𝑡𝐼𝑠
Substitute the given to the formula 𝑟 = (20,000)(4) 4000
Performing the operations r = 0.
Express your answer in percent r = 5%
Therefore, the rate of interest is 5%.
Example 3: Given: 𝑃 = ₱40,000., 𝐼𝑠 = ₱700, 𝑟 = 7%. Find time (𝑡).
Solution:
Use the formula in finding the time 𝑡 = 𝑃𝑟𝐼𝑠
Substitute the given to the formula 𝑡 = (40000)(0) 700
####### 𝐹 = 𝑃(1 + 𝑟𝑡) 𝐹 = 𝑃 + 𝐼𝑠
How are you going to express the time in years? ___________________
How much is the maturity value? _________________________
Activity 1.
Find the value of the required components in each item.
- Find the simple interest and maturity value if P = ₱13,000, r = 0% and t = 2 ½ years.
2. If Is = ₱625, r = 2% and t =3 years, find the present value
Activity 1.
Complete the table below by finding the unknown.
Principal Rate Time Interest Maturity Value ₱45,000 2% 2 years 1% 4 years ₱4, ₱105,000 3% ₱114,
Guide Questions:
For the first set of values a. What unknown variable will you solve first? b. What formula will you use to find the missing values?
For the second set of values a. Which among the missing components can be solved using the given? b. How will you solve the next missing component?
For the third set of values a. What formula will you use to find the missing value? b. Which component can be solved first using the given?
Activity 1.
Complete the table below by finding the unknown.
Principal Rate Time Interest Maturity Value ₱60,000 5% 3 years 1 Ω % 2 years ₱1, ₱20,000 9 mos. ₱20,
Read the paragraph carefully and supply the missing term/s in the blanks that will make it logical.
In doing a business transaction one of the essential things to consider is the interest because it will be the basis whether you have gained or lost. When the interest is computed based on the principal it is called ______________ its formula is ____. There are other components included in the simple interest formula such as principal or present value, rate, time, and maturity value. In finding the principal the formula ______________ will be used. Meanwhile the rate must be expressed in ________ and in finding its value given the simple interest, principal and time you will use the formula. Moreover, time should be expressed in ________. In a simple interest environment, the formula to be used in finding the time is _____________. Lastly maturity value can be obtained by adding the __________and _________ or if the simple interest is not given you can use the formula ___________________.
Money Matters Read and analyze the situation below then, answer the question that follows.
You are a new accounts clerk in Lucena Metropolitan Bank where you met Mr. and Mrs. Smith who are preparing for the education of their children in the future. You wanted to introduce to them the advantage of time deposit having the following features:
Option A: 1% interest annually in 3 years, Option B: 1% interest annually in 5 years Option C: 1% interest annually in 8 years
What I Have Learned
What I Can Do
The previous lesson reiterates the importance of simple interest in a certain transaction. Interest is a natural event in a business transaction, however not all interest is classified as simple interest some of them are considered compound interest.
This lesson will delve into compound interest and the different components involved in it such as present value and maturity value.
For you to begin considering the lesson on the previous module which is essential in obtaining success in this lesson. Compound interest is not like a simple interest wherein only the principal is considered in the computation this type of interest considers the principal and the accumulated past interest. The frequency of conversion, nominal rate, and rate of interest for each conversion period will also play an important role in this lesson.
You also learned from the previous lesson that in getting the maturity value the formula 𝐹 = 𝐼𝑠 + 𝑃 will be used and in finding the principal or present value given the interest and maturity value the formula 𝑃 = 𝐹 − 𝐼𝑠 can be employed.
Let us take the following example.
Example 1: Given: P = ₱35,000 and Is = ₱ 4,000, find F.
Solution:
F = ₱35,000 + ₱4,000 = ₱39,
Example 2: Given: F = ₱50,000 and P = ₱45,000, find Is.
Solution:
Is = ₱50,000 – ₱45,000= ₱5,
Example 3: Given Is = ₱2,000 and F = ₱23,000., find P.
Solution:
P = ₱23,000 - ₱2,000b= ₱21,
Lesson
2
Interest, Maturity, Future,
and Present Values in
Compound Interest
What’s In
Read and analyze the situation below.
Let’s Save
Michael is planning to apply for a loan in Quezon Cooperative Bank, he is already aware of the terms payment for his loan but when he is about to pass his application form and compare his computation with the terms of payment provided by the bank he notices some discrepancy.
To enlighten he asked some explanations why they have different computations and the bank gave him the detailed computation:
Initially at t = 0 ₱100, at t = 1 ₱100,000 (1) = ₱103, at t = 2 ₱103,000 (1) = ₱106, at t = 3 ₱106,090 (1) = ₱109,272. Questions
- Is Michael’s computation correct?
Is the bank’s computation fair? Why?
How much is the difference in the total amount to be paid between Michael’s computation and the bank’s computation?
Why do you think the bank’s computation yielded more interest?
Do you think the bank committed an error in the computation of the amount to be paid?
What’s New
Michael’s Computation Amount of Loan: ₱100, Interest rate: 3% Due Date: After 3 years Computation: I = (100, 000)(0(3) I = ₱9, Amount to be paid after 3 years ₱109,
Computation from the bank Amount of Loan: ₱100, Interest rate: 3%
Year 1 Year 2 Year 3 Int 3000 6090 9272. Amt 103,000 106,090 109,272.
where: 𝐼𝑐 = compound interest P = principal or present value F = maturity (future) value
To find the present value or principal of the maturity value F due in t years the formulas are:
or
Example 1: Given: P= ₱18,500, r = 3% and compounded annually for 3 years, find the maturity value (F) and the compound interest (Ic ).
Solution: Use the formula of maturity value 𝐹 = 𝑃(1 + 𝑟)𝑡
Substitute the given to the formula 𝐹 = 18,500(1 + 0) 3
Performing the operations F = ₱20,215.
Apply the formula of compound interest 𝐼𝑐 = 𝐹 − 𝑃
Substitute the value of F that you get and P 𝐼𝑐 = 20,215 − 18500
Performing the operations 𝐼𝑐 = ₱1,715.
Therefore, the maturity value is ₱20,215 and the compound interest ₱1,715.
Example 2: Given F = ₱15,000, r = 2% compounded annually for 4 years, find the present value (P).
Solution:
Use the formula in finding the present value 𝑃 = (1+𝑟)𝐹 𝑡
Substitute the given to the formula 𝑃 = (1+0) 150004
Performing the operations P= ₱13,857.
Therefore, the present value is ₱13,857.
####### 𝑃 =
####### 𝐹
####### (1 + 𝑟)𝑡 𝑃 = 𝐹(1 + 𝑟)
−𝑡
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:
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
Rate (j) of interest for each conversion period 𝑗 = 𝑖
(𝑚) 𝑚 =
𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛
Study the table below.
Situations m n 𝑖𝑚 j 2% compounded annually for 3 years
Annually m = 1
m =1, t = 3 n = (1)(3)=
####### 𝑖 1 = 0 𝑗 = 𝑖𝑚
####### 𝑚
𝑗 = 0 1 = 0.
2% compounded semi – annually for 3 years
Semi – annually m = 2
m = 2, t = 3 n = (2)(3)=
####### 𝑖 2 = 0 𝑗 = 0.
2 = 0.
2% compounded quarterly for 3 years
Quarterly m = 4
m = 4, t = 3 n =(4) (3)=
####### 𝑖 4 = 0 𝑗 = 0.
4 = 0.
2% compounded monthly for 3 years
Monthly m = 12
m = 12, t = 3 n = (12)(3) = 36
####### 𝑖 12 = 0 𝑗 = 0.
12 = 0̅
2% compounded daily for 3 years
Daily m = 365
m = 365, t = 3 n = (365(3) =
####### 𝑖 365 = 0 𝑗 = 0.
365
Since the rate for each conversion period is represented by j, then in t years, interest is compounded mt times. Thus, the formula of Maturity Value for interest compounding m times a year is:
where: F = maturity value P = present value
####### 𝐹 = 𝑃(1 + 𝑗)𝑛
Gen Math 11 Q2 Mod2 Interest-Maturity-Present-and-Future-Values-in-Simple-and-Compound-Interest Version 2-from-CE1-ce2-1
Course: Accountancy (BSA2)
University: Quezon City University
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