rework If P dollars are invested at a simple interest rate r (in decimals), the amount A that will be available after t years is $$ \mathrm{A}=\mathrm{P}+\mathrm{Prt} $$. if $$ \$ 400 $$ is invested at a rate of $$ 6 \% $$, how long will it be before the amount of money available is $$ \$ 736 $$ ?

Question

UpStudy AI · Accepted Answer

To solve the problem, we start with the formula for the amount $$ A $$ available after $$ t $$ years when investing $$ P $$ dollars at a simple interest rate $$ r $$:

$$
A = P + Prt
$$

### Known Conditions:
- $$ P = 400 $$ (the initial investment)
- $$ r = 0.06 $$ (the interest rate in decimal form)
- $$ A = 736 $$ (the amount available after $$ t $$ years)

### Step 1: Substitute the known values into the formula

We can substitute $$ P $$, $$ r $$, and $$ A $$ into the equation:

$$
736 = 400 + 400 \cdot 0.06 \cdot t
$$

### Step 2: Simplify the equation

First, we can simplify the equation:

$$
736 = 400 + 24t
$$

### Step 3: Isolate $$ t $$

Now, we will isolate $$ t $$ by first subtracting 400 from both sides:

$$
736 - 400 = 24t
$$

This simplifies to:

$$
336 = 24t
$$

### Step 4: Solve for $$ t $$

Now, divide both sides by 24 to find $$ t $$:

$$
t = \frac{336}{24}
$$

Calculating this gives:

$$
t = 14
$$

### Conclusion

It will take **14 years** for the amount of money available to reach \$736 when \$400 is invested at a 6% simple interest rate.
It will take 14 years for the investment to grow to \$736.

rework If P dollars are invested at a simple interest rate r (in decimals), the amount A that will be available after t years is \( \mathrm{A}=\mathrm{P}+\mathrm{Prt} \). if \( \$ 400 \) is invested at a rate of \( 6 \% \), how long will it be before the amount of money available is \( \$ 736 \) ?

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