Solve $S I=P(1+r t)$ for $P$.
$P=\frac{S I}{1+r t}$
Given the formula in the format to input into the calculator. Type your answer with a negative exponent
$P=$
Answer (2)
Divide both sides of the equation by ( 1 + r t ) to isolate P : P = 1 + r t S I .
Rewrite the expression using a negative exponent: P = S I ( 1 + r t ) − 1 .
The formula for P in terms of S , I , r , and t , expressed with a negative exponent is: P = S I ( 1 + r t ) − 1 .
Explanation
Understanding the Problem We are given the formula S I = P ( 1 + r t ) and asked to solve for P . This means we want to isolate P on one side of the equation.
Isolating P To isolate P , we need to divide both sides of the equation by ( 1 + r t ) . This gives us: 1 + r t S I = 1 + r t P ( 1 + r t ) 1 + r t S I = P So, we have P = 1 + r t S I .
Expressing with Negative Exponent Now, we need to express this result using a negative exponent. Recall that x 1 = x − 1 . Therefore, we can rewrite the expression as: P = S I ( 1 + r t ) − 1 This is the formula for P in terms of S , I , r , and t , expressed with a negative exponent.
Final Answer Therefore, the solution for P is S I ( 1 + r t ) − 1 .
Examples
Understanding how to solve for a specific variable in a formula is crucial in many real-life scenarios. For example, in finance, the simple interest formula S I = P ( 1 + r t ) relates simple interest ( S I ) to the principal amount ( P ), interest rate ( r ), and time ( t ). If you know the simple interest earned, the interest rate, and the time period, you can solve for the principal amount ( P ) to determine how much money was initially invested. This is a practical application of algebraic manipulation in financial planning and analysis.
To solve for P in the equation S I = P ( 1 + r t ) , we isolate P by dividing both sides by ( 1 + r t ) , resulting in P = 1 + r t S I . We then express it with a negative exponent as P = S I ( 1 + r t ) − 1 . The final answer is P = S I ( 1 + r t ) − 1 .
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