Calculate Principal Given Interest Rate and Final Balance
Calculate Principal Given Interest Rate and Final Balance is a skill on Pengi from Lesson 3-5: Solve Simple Interest Problems in Reveal Math, Accelerated.
Key Concepts
Property To find the principal ($P$) when given the final balance ($A$) and the simple interest rate ($r$) for one period, use the formula: $$P = \frac{A}{1 + r}$$ where $r$ is the interest rate expressed as a decimal.
Examples If an account has a final balance of 105 dollars after earning 5% interest, the principal is $P = \frac{105}{1 + 0.05} = \frac{105}{1.05} = 100$ dollars. If a loan requires a total repayment of 270 dollars with an 8% interest rate, the original loan amount (principal) is $P = \frac{270}{1 + 0.08} = \frac{270}{1.08} = 250$ dollars. If an investment grows to 560 dollars at a 12% interest rate, the starting principal is $P = \frac{560}{1 + 0.12} = \frac{560}{1.12} = 500$ dollars.
Explanation The final balance represents the original principal (100%) plus the interest earned. To find the principal, first add the interest rate to 100% and convert it to a decimal. Then, divide the final balance by this combined decimal value. This reverses the process of calculating the final balance to reveal the starting amount.
Common Questions
What is Calculate Principal Given Interest Rate and Final Balance?
Calculate Principal Given Interest Rate and Final Balance is a skill on Pengi from Lesson 3-5: Solve Simple Interest Problems in Reveal Math, Accelerated.
What grade level is Calculate Principal Given Interest Rate and Final Balance for?
Calculate Principal Given Interest Rate and Final Balance is part of the Grade 7 Math curriculum, covered in Reveal Math, Accelerated. It is designed for students studying Math at the Grade 7 level.
How can I learn Calculate Principal Given Interest Rate and Final Balance?
Pengi offers an AI-guided lesson for Calculate Principal Given Interest Rate and Final Balance that walks you through the key concepts step by step. The lesson is aligned to Reveal Math, Accelerated so the content matches what you see in class.
How do I practice Calculate Principal Given Interest Rate and Final Balance?
After learning the concept, use the Practice mode to work through targeted exercises on Calculate Principal Given Interest Rate and Final Balance. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Calculate Principal Given Interest Rate and Final Balance?
Calculate Principal Given Interest Rate and Final Balance is covered in Reveal Math, Accelerated, specifically in Unit 3: Solve Problems Involving Percentages under Lesson 3-5: Solve Simple Interest Problems. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Calculate Principal Given Interest Rate and Final Balance free to study on Pengi?
Yes, the core Learn and Practice modes for Calculate Principal Given Interest Rate and Final Balance are available for free on Pengi. No credit card is required to start studying.