/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 61 Solve each formula for the speci... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 61

Solve each formula for the specified variable.} \(I=P R T\) for \(P \quad\) (Simple interest)

Short Answer

Expert verified
\(P = \frac{I}{RT}\)

Step by step solution

01

Understand the Formula

The formula given is for simple interest: \(I = P R T\). This formula represents the interest \(I\) earned or paid over a period of time \(T\) on a principal amount \(P\) with an interest rate \(R\). The goal is to solve for the principal \(P\).
02

Isolate the Variable

Since we need to solve for \(P\), we need to rearrange the formula to get \(P\) by itself. Start by dividing both sides of the equation by \(RT\):\[P = \frac{I}{RT}\].
03

Write the Re-arranged Formula

After dividing both sides of the original equation by \(RT\), the re-arranged formula is:\(P = \frac{I}{RT}\). This formula indicates that the principal \(P\) is equal to the interest \(I\) divided by the product of the interest rate \(R\) and the time period \(T\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Simple Interest
Simple interest is a concept used in finance to calculate the additional amount earned or owed on money over time. This calculation is essential in many real-world scenarios, such as loans and investments.
At its core, the simple interest formula is straightforward:
  • \[I = P \cdot R \cdot T\]
Here is what these symbols mean:
  • \(I\) stands for interest, which is the money added to or owed in addition to the principal.
  • \(P\) is the principal amount, or the initial sum of money.
  • \(R\) represents the interest rate, which is usually given as a percentage.
  • \(T\) is the time period over which the interest is calculated.
What makes simple interest 'simple' is that it is calculated only on the original principal, not on any interest that accumulates over time. Therefore, the calculation does not compound or increase over successive periods.
Solving Equations in Simple Interest
To solve equations, particularly those involving simple interest, one must be comfortable with manipulating algebraic expressions.
This involves performing operations like multiplication, division, addition, or subtraction to both sides of an equation to isolate unknown variables.
This is crucial when you know certain values of a formula and need to find an unknown value.In our original equation, we are solving for the principal \(P\).
The given formula is:
  • \[I = P \cdot R \cdot T\]
To solve for \(P\), we rearrange the formula by isolating \(P\) on one side of the equation, which demands confidence in algebraic principles.
Isolating Variables in Algebra
Variable isolation is a fundamental skill in algebra.
It entails rearranging an equation to make a particular variable the subject, which is especially crucial when dealing with more complex problems.For the formula \(I = P \cdot R \cdot T\), to find \(P\), algebraic manipulation is necessary:
  • First, identify the term to isolate: here, it's \(P\).
  • Then, divide both sides by the product \(R \cdot T\) to get \(P\) alone:
    \[P = \frac{I}{R \cdot T}\]
This rearrangement tells us that the principal \(P\) is derived by dividing the interest \(I\) by the product of the rate \(R\) and time \(T\).Isolating variables like this allows one to express any variable in terms of others, a powerful tool for problem-solving.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the equation of the line satisfying the given conditions, giving it in slope-intercept form if possible. Through the origin, perpendicular to \(2 x+y=6\)

Worldwide gambling revenue from online betting was \(\$ 18\) billion in 2007 and \(\$ 24\) billion in \(2010 .\) (Source: Christiansen Capital Advisors.) (a) Find an equation of a line \(y=m x+b\) that models this information, where \(y\) is in billions of dollars and \(x\) is the year. (b) Use this equation to estimate online betting revenue in 2013.

Sketch the graph of \(f\) by hand. $$f(x)=3$$

Determine the domain \(D\) and range \(R\) of each relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown. $$\\{(5,1),(3,2),(4,9),(7,6)\\}$$

Using the variable \(x\), write each interval using set-builder notation. $$(-4,3)$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.