Solve the following formula for t.

Question

Upper A equals Upper U left parenthesis 1 plus rt right parenthesis
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Part 1
The solution is tequals
  
enter your response here. ​(Simplify your​ answer.)

Answer 1

To solve the equation \( A = U(1 + rt) \) for \( t \), follow these steps:

1. Isolate the term involving \( t \): \[ A = U(1 + rt) \] Dividing both sides by \( U \): \[ \frac{A}{U} = 1 + rt \]

2. Subtract 1 from both sides: \[ \frac{A}{U} - 1 = rt \]

3. Reorganize the left side: \[ \frac{A - U}{U} = rt \]

4. Finally, isolate \( t \): \[ t = \frac{\frac{A - U}{U}}{r} \] Simplifying it further: \[ t = \frac{A - U}{Ur} \]

Thus, the solution for \( t \) is: \[ t = \frac{A - U}{Ur} \]