Rosa wants to invest $$ \$ 4400 $$ in a savings account that pays $$ 7.1 \% $$ simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.

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To determine how long it will take for Rosa's investment to double in value with simple interest, we can use the formula for simple interest:

$$
A = P(1 + rt)
$$

Where:
- $$ A $$ is the amount of money accumulated after n years, including interest.
- $$ P $$ is the principal amount (the initial amount of money).
- $$ r $$ is the annual interest rate (decimal).
- $$ t $$ is the time the money is invested for in years.

In this case:
- $$ P = 4400 $$
- $$ A = 2 \times 4400 = 8800 $$ (since we want to double the investment)
- $$ r = 7.1\% = 0.071 $$

We need to solve for $$ t $$:

$$
8800 = 4400(1 + 0.071t)
$$

Now, let's simplify and solve for $$ t $$:

1. Divide both sides by $$ 4400 $$:

$$
2 = 1 + 0.071t
$$

2. Subtract 1 from both sides:

$$
1 = 0.071t
$$

3. Divide both sides by $$ 0.071 $$:

$$
t = \frac{1}{0.071}
$$

Now, let's calculate $$ t $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{0.071}$$
- step1: Convert the expressions:
  $$\frac{1}{\frac{71}{1000}}$$
- step2: Multiply by the reciprocal:
  $$\frac{1000}{71}$$
Calculating $$ t $$:

$$
t \approx 14.084507
$$

Rounding this to the nearest tenth, we find:

$$
t \approx 14.1
$$

Thus, it will take approximately **14.1 years** for Rosa's investment to double in value at a simple interest rate of $$ 7.1\% $$.
It will take approximately 14.1 years for Rosa's investment to double in value.

Rosa wants to invest \( \$ 4400 \) in a savings account that pays \( 7.1 \% \) simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.

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