Problem Solving, Variables, Simple Interest

When was George Polya born?

Born in Hungary in 1887

Where did George Polya finish his PhD

University of Budapest

When did Polya die and at what age?

Year 1985 at 98

George Polya wrote more than ___ mathematical papers and three books.

250

The most famous book of George Polya, translated into 15 languages and it is in this book where he introduced his four-step process for solving problems.

He was known as the Father of Modern Problem Solving.

George Polya

Polya's Four-step Process for Solving Problems:

1. Understand the Problem (Given, asked)

2. Devise a Plan (Number sentence, operation, strategy)

3. Carry out the Plan (Solution, answer)

4. Look back (Checking)

Read the problem and understand all the words in it. You may try to restate the problem in your own words. Identify the given information and the unknown in the problem. Know if the information given is enough to solve the problem and if there are extraneous information. Tell if the problem at hand is similar to problems you have solved before.

Understand the Plan

Find the connection between the given and the unknown in the problem. Choose the appropriate strategy/ies to solve the problem

Devise a plan

Use the strategy/ies that you have chosen to solve the problem. If one strategy did not work, you may choose a different strategy. Take time in solving the problem. If the correct answer was not obtained in the first trial, keep trying until you succeed in getting the right answer

Carry out the plan

Check if your answer is correct. Can you see a better solution? Are there other ways that you could have used to get the answer?

Look back

Problem Solving Strategies:

1. Draw a Picture/Diagram

2. Guess and Check or Guess and Test (Trial & Error)

3. Use a table or make a list

4. Find a pattern

5. Working backwards

Amount of money paid back by the borrower for using the borrowed money for a certain period of time

or

Money earned by the lender

Simple Interest

Investments or deposits in bank also earn…?

Interests

Calculating the simple interest involves:

1. The amount (principal)

2. Interest rate

3. Time

Formula for Simple Interest:

I = Prt

I = the interest earned

P = the principal

r = the rate of interest per year

t = the time (in years)

t = number of months/12

It is the sum of the principal and the interest

The final amount/maturity value (F) at the end of the term (t years)

Final amount formula:

F = P + I

F = P + Prt

F = P(1 + rt)

There are two types of simple interest:

1. Exact Simple Interest

2. Ordinary Simple Interest

In here, the interest is computed using 365 days in a year

Exact simple interest

In here, the interest is computed using 360 days in a year

Ordinary simple interest

It is the money you earn on both the money you put in (called the principal) and the interest that money has already earned.

Compound interest

Compound Interest Formula:

A = P(1 + r/n)^nt

A = final amount

P = principal deposit

R = annual interest rate

n = number of compounding periods

t = time (expressed in years)