Jon has $5,000 to invest in a savings account that has interest compounded annually. If he wants his money to double in eight years, what percent must the interest rate be on the account?


We can solve this problem using the **compound interest formula**:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money after interest.
- $ P $ is the initial principal (the amount invested).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times interest is compounded per year.
- $ t $ is the number of years.

Since Jon wants his money to double in 8 years, we know:
- $ A = 2P $
- $ P = 5000 $ (but we'll cancel it out later)
- $ t = 8 $
- $ n = 1 $ (since the interest is compounded annually)
- We need to find $ r $.

The equation becomes:

\[
2P = P \left(1 + r\right)^8
\]

Dividing both sides by $ P $:

\[
2 = (1 + r)^8
\]

To solve for $ r $, take the 8th root of both sides:

\[
1 + r = 2^{\frac{1}{8}}
\]

Now, subtract 1 from both sides:

\[
r = 2^{\frac{1}{8}} - 1
\]

Let me calculate the value of $ r $.The interest rate Jon needs for his money to double in 8 years, with interest compounded annually, is approximately **9.05%**.

Would you like a detailed explanation, or do you have any further questions?

Here are some related questions for deeper understanding:
1. How does the number of compounding periods per year affect the required interest rate?
2. What would happen if Jon wanted to double his money in 6 years instead of 8?
3. How can the compound interest formula be adjusted for continuous compounding?
4. What is the difference between simple and compound interest in long-term investments?
5. How can the rule of 72 be used to estimate the doubling time for investments?

**Tip:** When working with compound interest, small changes in the interest rate or compounding frequency can have a significant impact over long periods!

Jon has $5,000 to invest in a savings account that has interest compounded annually. If he wants his money to double in eight years, what percent must the interest rate be on the account?

Discover how to calculate the interest rate required to double an investment of $5,000 in 8 years using the compound interest formula. This problem explores key concepts in algebra and exponential functions, making it ideal for students in Grades 9-12.

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