Calculate Interest Rate Given Principal and Final Balance
This Grade 7 math skill from Reveal Math, Accelerated teaches students to solve for the interest rate when the principal, time, and final balance are known. By rearranging the simple interest formula I = Prt, students isolate the rate r and interpret it as a percentage in real-world contexts like loans and savings.
Key Concepts
Property To find the simple interest rate ($r$) when given the principal ($P$) and the final balance ($A$) for one period, first calculate the total interest ($I$), and then divide by the principal: $$I = A P$$ $$r = \frac{I}{P}$$.
Examples A savings account starts with a principal of 500 dollars and has a final balance of 525 dollars after one year. The interest is $525 500 = 25$ dollars. The interest rate is $\frac{25}{500} = 0.05$, or $5\%$. A loan has a principal of 1200 dollars and a total repayment (final balance) of 1272 dollars. The interest paid is $1272 1200 = 72$ dollars. The interest rate is $\frac{72}{1200} = 0.06$, or $6\%$.
Explanation When you know both the starting amount and the final balance, you can figure out the interest rate in two simple steps. First, subtract the principal from the final balance to determine the actual amount of interest earned or paid. Next, divide that interest amount by the principal to find the rate as a decimal. Finally, multiply by $100$ to express that decimal as a percentage.
Common Questions
How do you calculate the interest rate from principal and final balance?
Find the interest earned (I = A - P), then use r = I / (P × t) to find the rate, where P is principal, t is time, and I is total interest.
What formula gives you the interest rate?
Rearranging I = Prt gives r = I / (Pt). Express the result as a decimal and multiply by 100 to get the percentage rate.
Why would you need to find the interest rate?
Knowing the interest rate helps compare financial products like savings accounts and loans to determine which offers better terms.
What units is the interest rate expressed in?
The interest rate is expressed as a percentage per year (annual rate) in most simple interest problems.
Where is this skill covered in Reveal Math Accelerated?
Calculating interest rate from principal and final balance is a Grade 7 topic in the Reveal Math, Accelerated textbook.