Grade 7

Intermediate

8 min

Lesson 11 of 12

The Simple Interest Formula

Not Started

Introduction to financial literacy by calculating interest earned or owed over time.

Imagine putting $100 in a shoebox versus putting it in a bank account. After one year, the shoebox still has$ 100, but the bank account might have $105. Where did that extra$ 5 come from, and how can you predict exactly how much 'free money' you'll earn?

Learning Objectives

1.Identify and define the variables in the simple interest formula $I = Prt$ .
2.Calculate the amount of interest earned or owed using decimal conversions for rates.
3.Determine the total balance of an account by combining the principal and the interest.

The Ingredients of Interest

To calculate Simple Interest, we use the formula $I = Prt$ . Think of this like a recipe where every letter represents a specific 'ingredient' of your investment. Principal ( $P$ ) is the starting amount of money you deposit or borrow. The Rate ( $r$ ) is the percentage charged or earned, which must always be converted into a decimal before calculating (for example, $5\% = 0.05$ ). Finally, Time ( $t$ ) is the duration the money is left alone, measured specifically in years. When you multiply these three together, you get the Interest ( $I$ ), which is the extra money earned or paid.

Suppose you deposit $\$ 500 $into a savings account with a$ 3\% $simple interest rate for$ 2$ years. How much interest will you earn?

1. Identify variables: $P = 500$ , $r = 0.03$ (converted from $3\%$ ), $t = 2$ . 2. Set up the formula: $I = 500 \cdot 0.03 \cdot 2$ . 3. Multiply $P$ and $r$ : $500 \cdot 0.03 = 15$ . 4. Multiply by $t$ : $15 \cdot 2 = 30$ . 5. The interest earned is $\$ 30$.

Quick Check

If a bank offers a $4\%$ interest rate, what value should you plug into the formula for ' $r$ '?

Divide the percentage by 100 to get the decimal.

Answer

0.04

The Big Picture: Total Balance

Finding the interest is often just the first step. Usually, you want to know the Total Balance (

A

), which is the total amount in the account after the interest has been added. To find this, you simply add the interest you calculated (

I

) back to your original principal (

P

). The formula looks like this:

A = P + I

This tells you the 'bottom line'—exactly how much cash is available to spend or how much you total owe back on a loan.

You borrow $\$ 2,000 $to buy a used scooter at a$ 6\% $simple interest rate. You plan to pay it back in$ 3$ years. What is the total amount you will pay back?

1. Calculate Interest ( $I$ ): $I = 2000 \cdot 0.06 \cdot 3$ . 2. $I = 120 \cdot 3 = 360$ . 3. Calculate Total Balance ( $A$ ): $A = P + I$ . 4. $A = 2000 + 360 = 2360$ . 5. You will pay back a total of $\$ 2,360$.

Quick Check

If you earn $\$ 50 $in interest on a$ \ $1,000$ deposit, what is your total balance?

Use the formula

A = P + I

Answer

$1,050

Time is of the Essence

The variable $t$ in our formula must be in years. But what if a problem gives you time in months? Because there are $12$ months in a year, you must convert months to a fraction of a year. For example, $6$ months is $\frac{6}{12}$ or $0.5$ years. If you forget this step and plug '6' into the formula instead of '0.5', the math will think you left the money in the bank for 6 full years, giving you a very wrong (and much too large) answer!

You put $\$ 1,200 $into an account with an$ 8\% $interest rate, but you only leave it there for$ 9$ months. What is the total balance?

1. Convert time to years: $t = \frac{9}{12} = 0.75$ . 2. Calculate Interest: $I = 1200 \cdot 0.08 \cdot 0.75$ . 3. $I = 96 \cdot 0.75 = 72$ . 4. Calculate Balance: $A = 1200 + 72 = 1272$ . 5. The total balance is $\$ 1,272$.

Key Takeaways

1The simple interest formula is $I = Prt$ , where $I$ is interest, $P$ is principal, $r$ is rate, and $t$ is time.
2Always convert the interest rate percentage to a decimal (e.g., $7\% = 0.07$ ).
3Time ( $t$ ) must be expressed in years; use fractions like $\frac{m}{12}$ for months.
4The total balance ( $A$ ) is found by adding the interest to the principal: $A = P + I$ .

Quick Check

Multiple Choice

What does the 'P' represent in the formula $I = Prt$ ?

Multiple Choice

Calculate the interest earned on $\$ 400 $at a$ 5\% $rate for$ 3$ years.

True/False

If a problem mentions '18 months', you should use $t = 1.5$ in the formula.

What's Next?

Review Tomorrow

In 24 hours, try to write down the simple interest formula and explain what each of the four letters stands for without looking at your notes.

Practice Activity

Find a real-world 'High Yield Savings Account' rate online (usually around 4-5%) and calculate how much interest you would earn in 5 years if you deposited $1,000 today.

Browse

Browse

The Simple Interest Formula

Learning Objectives

The Ingredients of Interest

The Big Picture: Total Balance

Time is of the Essence

Key Takeaways

Quick Check

What's Next?

The Simple Interest Formula

Learning Objectives

The Ingredients of Interest

The Big Picture: Total Balance

Time is of the Essence

Key Takeaways

Quick Check

What's Next?