Finding a final amount in a word problem on exponential growth or decay
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A principal of $1500 is invested at 5.25% Interest, compounded annually. How much will the investment be worth after 13 years?
Use the calculator provided and round your answer to the nearest dollar.

To solve this problem, we need to use the formula for compound interest:

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

where:  
- $ A $ is the final amount (what we're solving for),  
- $ P $ is the principal (initial amount), which is $1500,  
- $ r $ is the annual interest rate (as a decimal), which is 5.25% or 0.0525,  
- $ n $ is the number of times interest is compounded per year (since it is compounded annually, $ n = 1 $),  
- $ t $ is the time the money is invested for, which is 13 years.  

Plugging in the values:

\[
A = 1500 \left(1 + \frac{0.0525}{1}\right)^{1 \times 13}
\]

Let's calculate this step-by-step.The investment will be worth **$2,917** after 13 years, when rounded to the nearest dollar.

Would you like more details on the calculation or have any questions?

Here are 5 related questions that you might find useful:
1. What would the final amount be if the interest were compounded semi-annually instead?
2. How does compounding frequency affect the final amount in an investment?
3. What would the final amount be if the principal was $2000 instead of $1500, with the same interest rate and time period?
4. How can we calculate the time required for an investment to double with compound interest?
5. What happens to the final amount if the interest rate changes from 5.25% to 6%?

**Tip:** Understanding how the compounding period affects growth can help you optimize investment decisions!

Learn how to calculate compound interest with an initial investment of $1500 at an annual interest rate of 5.25% over a period of 13 years. The investment will be worth $2,917 after compounding annually. Explore related questions about compounding frequency and investment strategies.

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