Introduction to Simple Interest - Sixth Grade Mathematics

Simple interest is the fee paid for borrowing money or the financial return earned on invested savings, calculated through a linear formula connecting principal, interest rate, and time.

The Core Concept of Interest

When you deposit money into a savings account, the bank pays you interest for the privilege of using your funds. When you borrow money from a lender (such as taking a car loan or student loan), you must pay interest to the lender for the use of their money. Simple interest calculates interest solely on the original starting balance.

The Simple Interest Formula:
                         I = P * r * t

Where:
- I = Interest:  The amount of money earned or paid ($).
- P = Principal: The initial amount of money deposited or borrowed ($).
- r = Rate:      The annual interest rate (MUST be written as a decimal!).
- t = Time:      The duration of the loan or investment in YEARS.

Deconstructing the Formula Variables

Each variable in the simple interest formula must be converted into standard mathematical units before computing:

+-------------------------------------------------------------------------+
|                  DECONSTRUCTING THE VARIABLES OF I = P * r * t          |
+-------------------+-----------------------+-----------------------------+
| Variable          | Unit Requirement      | Transformation Rule         |
+-------------------+-----------------------+-----------------------------+
| Principal (P)     | Dollars and cents     | Starting money ($)          |
+-------------------+-----------------------+-----------------------------+
| Rate (r)          | Annual decimal rate   | Convert percent to decimal: |
|                   |                       | 6% -> 0.06;  4.5% -> 0.045  |
+-------------------+-----------------------+-----------------------------+
| Time (t)          | Must be in YEARS      | If given in months, divide  |
|                   |                       | by 12: 6 months = 6/12 = 0.5|
+-------------------+-----------------------+-----------------------------+

Calculating Total Future Balance

Interest represents only the fee or earnings. To calculate the total balance in an account or the total repayment due on a loan, add the interest earned back to the starting principal.

Total Balance Formula:
                         A = P + I   (or  A = P + P*r*t)

Where:
- A = Total Accumulated Amount (Future Value)
- P = Principal
- I = Interest Earned or Owed

Worked Example: You deposit $500 in a savings account earning 4% simple
interest per year. How much interest is earned after 3 years, and what
is the total account balance?

Step 1: Identify values:
        P = $500
        r = 4% = 0.04
        t = 3 years

Step 2: Calculate Interest using I = P * r * t:
        I = 500 * 0.04 * 3
        I = 20 * 3 = $60 interest.

Step 3: Calculate Total Balance A = P + I:
        A = $500 + $60 = $560.
Conclusion: The interest earned is $60, and the final balance is $560.

Managing Time Expressed in Months

When time is stated in months, you must express it as a fraction of a year by dividing by 12. Never insert the raw number of months directly into the formula! If a loan lasts 9 months: t = 9/12 = 3/4 = 0.75 years. If an investment lasts 18 months: t = 18/12 = 1.5 years.

Exercises

Exercise 1. Calculate the simple interest earned on a principal deposit of $1,200 at an annual interest rate of 5% over 4 years.

Exercise 2. A borrower takes out a personal loan of $2,500 at a 6% annual simple interest rate. How much total interest is owed if the loan is repaid after 18 months, and what is the total repayment amount?

Exercise 3. An investor deposits $800 into a certificate of deposit. After 2 years, the account has earned $48 in simple interest. What was the annual interest rate of the account?

Solutions

Solution to Exercise 1. Identify values: P = 1,200; r = 5% = 0.05; t = 4 years. Apply formula: I = P * r * t = 1,200 * 0.05 * 4. Compute: 1,200 * 0.05 = 60; 60 * 4 = 240. The simple interest earned is $240.

Solution to Exercise 2. Identify values: P = 2,500; r = 6% = 0.06. Convert time from months to years: t = 18 / 12 = 1.5 years. Apply formula: I = 2,500 * 0.06 * 1.5. Compute: 2,500 * 0.06 = 150; 150 * 1.5 = 225 dollars interest. To find total repayment due: A = P + I = 2,500 + 225 = $2,725. The total interest owed is $225, and the total repayment amount is $2,725.

Solution to Exercise 3. Identify values: P = 800; I = 48; t = 2 years; r is unknown. Use formula: I = P * r * t. Substitute known values: 48 = 800 * r * 2. Multiply known factors: 48 = 1,600 * r. Solve for r by dividing both sides by 1,600: r = 48 / 1,600. Simplify: divide top and bottom by 16: 3 / 100 = 0.03. Convert the decimal rate to a percent: 0.03 * 100 = 3%. The annual interest rate was 3%.