3. Home Renovation Fund
Sarah is saving $40,000 to renovate her home. She plans to invest this money in an account with a 6% interest rate compounded annually for the next 5 years. How much money will Sarah have after 5 years to complete her home renovation?

FV=PV(1.00+I)n, where:

FV = Future Value
PV = Present Value
I = Interest rate (as a decimal)
n = Number of periods
 

Step-by-Step Solution:
Write the formula:
Add the interest rate to 1:FV=
Calculate:
Multiply the result by the present value
Final Answer: The future value of Sarah’s account after 5 years will be $



To determine how much money Sarah will have after 5 years, we'll use the given formula for future value (FV):

\[
FV = PV \times (1 + I)^n
\]

Where:
- $ PV = 40,000 $ (Present Value)
- $ I = 6\% = 0.06 $ (Interest rate as a decimal)
- $ n = 5 $ (Number of periods, since the interest is compounded annually for 5 years)

### Step-by-Step Solution:

1. **Write the formula:**
   \[
   FV = PV \times (1 + I)^n
   \]
   
2. **Add the interest rate to 1:**
   \[
   1 + I = 1 + 0.06 = 1.06
   \]

3. **Calculate:**
   \[
   FV = 40,000 \times (1.06)^5
   \]

4. **Evaluate $ (1.06)^5 $:**
   \[
   (1.06)^5 = 1.338225
   \]

5. **Multiply the result by the present value:**
   \[
   FV = 40,000 \times 1.338225 = 53,529
   \]

### Final Answer:
The future value of Sarah's account after 5 years will be approximately **$53,529**.

Would you like further details or any clarifications?

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Here are 5 related questions to expand on this topic:
1. What would Sarah's future value be if the interest rate were compounded quarterly instead of annually?
2. How would the future value change if Sarah invests for 10 years instead of 5 years at the same interest rate?
3. What is the formula for continuous compounding, and how would it apply to Sarah's investment?
4. If Sarah only had $30,000 to invest, what would the future value be after 5 years with the same conditions?
5. How would the result change if the interest rate were 8% instead of 6%?

**Tip:** Compounded interest grows faster the more frequently it is compounded, making a big difference over time!

Sarah is saving $40,000 to renovate her home. She plans to invest this money in an account with a 6% interest rate compounded annually for the next 5 years. How much money will Sarah have after 5 years to complete her home renovation?

Discover how to calculate the future value of a $40,000 investment at a 6% annual interest rate, compounded for 5 years. This problem covers key financial math concepts such as compound interest and exponential growth, providing a clear, step-by-step solution. Ideal for high school students in Grades 9-12.

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