Simple Interest Formulas for K-12 Students
Elementary School (Grades K-5)
Introduction to Simple Interest:
Simple interest is money that you earn on savings or pay on loans.
\(Interest = Money \times Rate \times Time\)
Middle School (Grades 6-8)
Basic Simple Interest Formula:
\(I = P \times r \times t\)
Where:
- \(I\) = Interest earned or paid
- \(P\) = Principal (the initial amount of money)
- \(r\) = Rate of interest (as a decimal)
- \(t\) = Time (usually in years)
Total Amount Formula:
\(A = P + I\)
Where:
- \(A\) = Total amount (principal plus interest)
High School (Grades 9-12)
Expanded Simple Interest Formula:
\(A = P(1 + rt)\)
Finding the Principal:
\(P = \frac{I}{r \times t}\)
Finding the Rate of Interest:
\(r = \frac{I}{P \times t}\)
Finding the Time:
\(t = \frac{I}{P \times r}\)
Finding Principal from Total Amount:
\(P = \frac{A}{1 + rt}\)
Example Problems
Elementary Example:
If you save $100 for 1 year at a 5% interest rate, how much interest will you earn?
Solution: \(Interest = $100 \times 0.05 \times 1 = $5\)
Middle School Example:
A $500 loan has a 6% annual interest rate for 2 years. Find the interest and the total amount to be repaid.
Solution:
\(I = P \times r \times t = $500 \times 0.06 \times 2 = $60\)
\(A = P + I = $500 + $60 = $560\)
High School Example:
How long will it take for $1,200 to earn $180 in interest at an annual rate of 5%?
Solution:
\(t = \frac{I}{P \times r} = \frac{$180}{$1,200 \times 0.05} = \frac{$180}{$60} = 3 \text{ years}\)
Conversion Formulas
Converting Annual Rate to Monthly Rate:
\(r_{monthly} = \frac{r_{annual}}{12}\)
Converting Years to Months:
\(t_{months} = t_{years} \times 12\)
Converting Percentage to Decimal:
\(r_{decimal} = \frac{r_{percentage}}{100}\)