Make 'P' the subject in the formula A = P (1+r)
Answer (2)
To isolate 'P' in the formula A = P ( 1 + r ) , divide both sides by ( 1 + r ) to yield P = 1 + r A . This allows us to calculate the principal amount necessary to achieve a certain total given an interest rate. Understanding this process is essential in algebra and finance.
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Divide both sides of the equation by ( 1 + r ) .
Simplify the equation to isolate P .
Express P in terms of A and r .
The final formula is: P = 1 + r A
Explanation
Understanding the Problem We are given the formula A = P ( 1 + r ) and our goal is to isolate P on one side of the equation. This means we want to rewrite the formula so that it expresses P in terms of A and r .
Isolating P To isolate P , we need to undo the multiplication by ( 1 + r ) . We can do this by dividing both sides of the equation by ( 1 + r ) .
Performing the Division Dividing both sides of A = P ( 1 + r ) by ( 1 + r ) gives us: 1 + r A = 1 + r P ( 1 + r )
The Final Formula Since 1 + r P ( 1 + r ) = P , we have: 1 + r A = P Therefore, we can write P as: P = 1 + r A
Examples
Imagine you want to know how much money ( P ) you need to invest initially to reach a certain amount ( A ) after one year, given an interest rate ( r ). By rearranging the formula A = P ( 1 + r ) to solve for P , you can easily calculate the principal amount needed. For example, if you want to have A = $110 after one year with an interest rate of r = 10% = 0.1 , you can use the formula P = 1 + r A = 1 + 0.1 110 = 1.1 110 = $100 . This shows that you need to invest $100 initially. This concept is widely used in finance for calculating present values and investment planning.
