Simple Interest Principles and Formulas

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What must be true for a conjunction statement to be true?

Neither proposition can be true.

Both propositions must be true. (correct)

Either proposition must be true.

At least one proposition must be false.

In a disjunction statement, when is the whole statement true?

At least one proposition must be true. (correct)

Both propositions must be true.

Only one proposition can be true.

Both propositions must be false.

What is the key word associated with conditional statements?

And

If and only if

If...then (correct)

If...or

What does the biconditional 'if and only if' imply about the proposed statements?

Both statements must be either true or false. Signup and view all the answers

What does negation do to a statement?

Makes a true statement false. Signup and view all the answers

Which symbol represents disjunction?

∨ Signup and view all the answers

In the statement 'You will pass the exam if and only if you study', what is the implication?

Not studying guarantees failing the exam. Signup and view all the answers

Which logical operator requires that both parts must be true for the entire statement to be true?

Conjunction Signup and view all the answers

Which logical statement will always be true, regardless of the truth of its components?

A conditional statement with a false antecedent. Signup and view all the answers

What is the symbol used for negation?

~ Signup and view all the answers

What is the formula for calculating simple interest?

I = Prt Signup and view all the answers

Which of the following represents Maturity Value?

A = P + I Signup and view all the answers

To convert an annual interest rate of 8% to decimal form, what should it be written as?

0.08 Signup and view all the answers

If a loan of ₱150,000 is taken for 2 years at an interest rate of 12%, how much total amount will be owed at maturity?

₱180,000 Signup and view all the answers

How would you express the time in years if you have a loan for 9 months?

0.75 years Signup and view all the answers

What formula would you use to find the principal if you know the total maturity value, interest, and rate?

P = A/(1 + rt) Signup and view all the answers

Which type of interest is based on a 360-day year and is commonly used by banks?

Ordinary Interest Signup and view all the answers

For an investment that earns $200 in simple interest over one year at a rate of 5%, what was the principal amount?

$2,000 Signup and view all the answers

Which of the following statements represents a disjunction?

I will have chocolate or vanilla ice cream. Signup and view all the answers

What is the symbolic representation of 'It is not true that I am hungry'?

∼p Signup and view all the answers

What is the time period in years for 150 days using exact interest calculations?

0.41 years Signup and view all the answers

Which statement correctly illustrates a conditional relationship?

If he has a green thumb, then he is not a senior citizen. Signup and view all the answers

In the statement 'You will pass if and only if you study', what logical relationship is represented?

Biconditional Signup and view all the answers

Which of the following is a correct symbolic representation for 'It is not the case that he has a green thumb or he is a senior citizen'?

∼(p∨q) Signup and view all the answers

Which statement can be rearranged as a conjunction?

It is not raining, and the sun is shining. Signup and view all the answers

What type of logical connection does the statement 'If he has a green thumb, then he is a senior citizen' represent?

Conditional Signup and view all the answers

Which symbolic representation corresponds to the statement 'He has a green thumb and he is not a senior citizen'?

p∧∼q Signup and view all the answers

What is represented by the statement 'If he is a senior citizen, then he has a green thumb; and if he has a green thumb, then he is a senior citizen'?

p↔q Signup and view all the answers

Which of the following symbolizes a negation?

∼p Signup and view all the answers

What amount of interest is calculated using ordinary interest for a principal of ₱200,000 at a 10.5% rate over 180 days?

₱10,500 Signup and view all the answers

How much interest is charged using exact interest for a ₱200,000 loan at a 10.5% rate over 180 days?

₱10,356.16 Signup and view all the answers

What is the maturity value for a loan of ₱3,000 at 14% interest for 6 months?

₱3,210 Signup and view all the answers

If the interest is calculated using a 360-day year, what is the correct way to convert the time from days to years?

t = 180/360 Signup and view all the answers

Which statement correctly describes a simple proposition?

A statement expressing one clear idea without connecting words. Signup and view all the answers

In the context of math interest calculations, which formula is used to find the interest?

I = Prt Signup and view all the answers

What type of interest calculation involves using a 365-day year?

Exact Interest Signup and view all the answers

How do you convert percentages to decimals for calculations?

Divide by 100 Signup and view all the answers

What is the approximate time in years for a loan of 180 days using a 365-day year?

0.493 years Signup and view all the answers

Which statement best defines a compound proposition?

Combines two or more simple propositions with connecting words. Signup and view all the answers

Study Notes

Simple Interest

Principal (P): The initial amount borrowed or invested. Also called face value or present value.
Rate (r): The annual interest rate, expressed as a decimal (e.g., 8% = 0.08).
Time (t): The length of time the money is borrowed or invested, usually measured in years. Months are divided by 12, days may use 360 (ordinary) or 365 (exact) days.
Interest (I): The amount paid or earned for using money. Calculated as I = Prt
Maturity Value (A): The total amount paid or received at the end of the loan/investment period. Calculated as A = P + I, or A = P(1 + rt).
Formulas:
- Simple Interest: I = Prt
- Maturity Value: A = P + I or A = P(1 + rt)
- Other derived formulas:
  - Principal: P = A / (1 + rt)
  - Rate: r = (A − P)/(Pt)
  - Time: t = (A − P)/(Pr)

Ordinary vs. Exact Interest

Ordinary Interest: Based on a 360-day year, commonly used by banks. Time is calculated as t = days/360
Exact Interest: Based on a 365-day year. Time is calculated as t = days/365

Propositions and Logic

Proposition: A statement that can be either true or false, but not both simultaneously.
Simple Proposition: A statement with one clear idea, without connecting words (e.g., "She is happy").
Compound Proposition: A statement combining multiple simple propositions using connecting words like "and," "or," "if...then" (e.g., "It is raining, and I am going to the store").
Connectives:
- Conjunction (AND): Both parts must be true for the whole statement to be true. Symbol: ^
- Disjunction (OR): At least one part must be true for the whole statement to be true. Symbol: v
- Conditional (If...Then): If the first part is true, then the second part is also true. The whole statement can still be true if the first part is false. Symbol: →
- Biconditional (If and Only If): Both parts must be either both true or both false. Symbol: ↔
- Negation (Not): Denies a statement. Makes a true statement false and vice versa Symbol: ~

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz explores the fundamental concepts of simple interest, including key terms such as principal, rate, and time. You'll learn how to calculate interest and maturity value using various formulas. Test your understanding of both ordinary and exact interest calculations.