To solve for $t$ in the formula $A = P(1 + rt)$, we'll rearrange the formula to isolate $t$.

Given:

• $A = 1057$
• $P = 700$
• $r = 17\% = 0.17$

Formula:

$A = P(1 + rt)$

Steps:

1. Substitute the given values into the equation: $1057 = 700(1 + 0.17t)$

2. Divide both sides by 700 to isolate the term with $t$: $\frac{1057}{700} = 1 + 0.17t$

3. Calculate the left-hand side: $1.51 = 1 + 0.17t$

4. Subtract 1 from both sides: $0.51 = 0.17t$

5. Divide both sides by 0.17 to solve for $t$: $t = \frac{0.51}{0.17} \approx 3$

Answer:

$t \approx 3 \text{ years}$

Would you like more details on any step? Here are some related questions:

1. How do you rearrange equations to solve for a specific variable?
2. What is the interpretation of the time $t$ in financial calculations?
3. How does changing the interest rate $r$ affect the time $t$?
4. Can this formula be used for compound interest? Why or why not?
5. What happens to the value of $t$ if the principal $P$ increases?

Tip: When dealing with percentage rates in formulas, always convert the percentage to a decimal by dividing by 100.