inda Baer has already saved ​$3 comma 554 to buy a used vehicle. Ignoring taxes and assuming her money is invested in a money market account earning 7 percent compounded​ annually, how long will it take to buy a car that costs ​$6 comma 533​?
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Ignoring taxes and assuming her money is invested in a money market account earning 7​% compounded​ annually, to save  the money to buy a car that costs ​$6 comma 533 will take

enter your response here years.

To solve this problem, we need to calculate how long it will take for Linda Baer's savings to grow from $3,554 to $6,533 at an annual interest rate of 7%, compounded annually. 

The formula for compound interest is:

\[
A = P(1 + r)^t
\]

Where:
- $ A $ is the future value (in this case, $6,533).
- $ P $ is the present value or initial savings (in this case, $3,554).
- $ r $ is the interest rate per period (7% or 0.07).
- $ t $ is the number of years it will take to reach the future value.

We need to solve for $ t $, the number of years.

Rearranging the formula to solve for $ t $:

\[
t = \frac{\ln(A / P)}{\ln(1 + r)}
\]

Now we can plug in the values:

\[
t = \frac{\ln(6533 / 3554)}{\ln(1 + 0.07)}
\]

Let me calculate that.It will take approximately 9 years for Linda Baer's savings to grow to $6,533 at an annual interest rate of 7%, compounded annually.

Would you like more details or have any further questions?

Here are five related questions to deepen your understanding:
1. How does compound interest differ from simple interest?
2. What happens if the interest is compounded more frequently, such as monthly or quarterly?
3. How does the amount of time change if the interest rate increases to 8%?
4. How much would Linda need to save upfront to buy the car in 5 years instead of 9?
5. What are other investment options with higher rates of return?

**Tip:** The power of compounding is significant over time; even small changes in interest rates can greatly affect the outcome.

Linda Baer has already saved $3,554 to buy a used vehicle. Ignoring taxes and assuming her money is invested in a money market account earning 7% compounded annually, how long will it take to buy a car that costs $6,533?

Discover how long it will take for $3,554 to grow to $6,533 with compound interest at 7%. Learn key mathematical concepts like compound interest, exponential growth, and logarithms. Ideal for students in Grades 9-12 looking to understand real-world applications of math.

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