Simple Interest: A Deeper Dive

Simple interest happens when you borrow some money from someone for a short period of time, and they get paid back later with a little profit (or interest) for them. 

What do I need to understand before reading this blog?

• Arithmetic: Adding and multiplying

• Algebra: Applying values to variables, Factoring, and the Distributive Property over Addition

Click here if you need help with these prerequisites

Click here for help with Pre-Algebra and Algebra.

Check out moment.of.math for Algebra practice.

To learn more about the Financial Math Series, please see the first blog entry: Introduction to Basic Financial Concepts

See the below example showing how to use the moment.of.math scratchpad.

What is Simple Interest?

Simple interest is just as it sounds.  It’s simple.  Simple interest usually happens when timelines are relatively short, or when a loan is generated by a friend or family member who just wants to keep the math simple.  You ask to borrow some money from someone, and they get paid back later with a little profit (or interest).  The formula for calculating the Future Value of the loan as a function of Present Value and Interest is:

F = P * (1+R)

In this formula,

• F = the Future Value of the loan or investment

• P = the Present Value of the loan or investment

• R = the Interest Rate for the loan or investment in a decimal form of percent (%/100)

Don't understand this equation? Click here to see how to derive the Simple Interest equation "F = P*(1+R)" using the moment.of.math scratchpad

As a practice problem, let’s assume you ask to borrow $100 from a friend and you tell them you can pay them back in a month when you get your next paycheck.  They want 10% interest in the loan.  The first thing you need to know is how much money you need to collect to pay your friend back in a month.  This is a matter of adding the loan amount to the interest owed. Use this equation:

F = P + I

Where:

• F = the Future Value of the loan

• P = the Present Value of the loan

• I = the amount of Interest

We also need to know that the Interest is the Present Value "P" times the Interest Rate, “R”.

I = P * R

Where:

• I = the Interest generated in the loan or investment

Simple Interest Derivation:

Below the moment.of.math scratchpad shows how the equation is set up.

Note above how the green dots track your progress and shows you are on the right track. The double check mark confirms that your answer and all your math is correct.

*Note: You can also right-click on the “P” and select the value “100” from the “Substitute” menu at the bottom of the list.  Then right-click on the “R” and select the value “.1” from the “Substitute” menu at the bottom of the list. 

Note: There are many ways to set up and reduce the equations starting with Step 5.  Try different methods to figure out the way that works best for you.

We’ve now proven that "F = P+P*R", and we can reduce that equation to

F = P* (1+R)

Note, if you don't understand how we jumped from "P+P*R" to "P*(1+R)" please brush up on Factoring and the Distributive Property over Addition. Click here to learn more.

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Simple Interest: Worked Example Problem

Problem: Bob needs to pay an unexpected vet bill.  The bank offers to loan him the $250 that he needs for a month at 5% interest.  Using the equation "F=P*(1+R)", determine how much Bob owes next month.

Note above how the green dots track your progress and shows you are on the right track. The double check mark confirms that your answer and all your math is correct.

*Note: You can also duplicate a line by holding down the “Shift” key and hit the “Enter” key. 

**Note: You can also right-click on the “P” and select the value “250” from the “Substitute” menu at the bottom of the list.  Then right-click on the “R” and select the value “.05” from the “Substitute” menu at the bottom of the list. 

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Try the below Simple Interest problem yourself!

Problem: Kathy needs to pay an unexpected car repair bill.  She finds someone who will loan her the $555 that she needs for a month for 10% interest.  Using the equation "F=P* (1+R)", determine how much Kathy owes next month.

Click here to see the answer

STEP-BY-STEP SOLUTION

Setup:

1. "Let" statement assigns 555 to "P"

2. "Let" statement assigns .1 to "R" (because 10% = 10/100)

3. "Let" statement defines the formula "F=P*(1+R)"

Begin Work:

4. Recreate the math equation by clicking on the 3^rd line then right-click and select “Start from numbered equation …” then select the line for “F=P*(1+R)”.  This will pop that equation at the bottom of your work.*

Substitute the variables with their values:

5. Replace the “P” with “555” and the “R” with “.1” in this 4^th line.**

Finally, calculate the answer:

6. Click anywhere into the last line that contains only numbers and right-click.  Select “Calculate Line” and the answer 610.5 pops up in the final line. 

Remember that the green dots track your progress and shows you are on the right track. The double check mark confirms that your answer and all your math is correct.

*Note: You can also duplicate a line by holding down the “Shift” key and hit the “Enter” key. 

**Note: You can also right-click on the “P” and select the value “555” from the “Substitute” menu at the bottom of the list.  Then right-click on the “R” and select the value “.1” from the “Substitute” menu at the bottom of the list. 

Catch your algebra mistakes before they cost you

The scratchpad in this guide runs on moment.of.math — a free Chrome extension that checks your algebra line by line, on any problem. It can generate new variations problems, so you can get as much practice as you need. On many homework sites, it automatically detects the math on the page, so you don't have to copy anything over. Try it on tonight's homework.

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