If you invest $100 today and wait for 10 years with a 5% interest rate, what is the value of your investment in 10 years?



To determine the value of your investment after 10 years with a 5% interest rate, we can use the formula for compound interest:

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

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

Assuming the interest is compounded annually (n=1):

\[ A = 100 \left(1 + \frac{0.05}{1}\right)^{1 \times 10} \]
\[ A = 100 \left(1 + 0.05\right)^{10} \]
\[ A = 100 \left(1.05\right)^{10} \]

Now we calculate $ 1.05^{10} $:

\[ 1.05^{10} \approx 1.62889 \]

So,

\[ A = 100 \times 1.62889 \]
\[ A \approx 162.89 \]

The value of your investment after 10 years with a 5% interest rate compounded annually would be approximately $162.89.

Would you like more details or have any questions?

Here are some related questions you might be interested in:
1. How does the frequency of compounding affect the future value of an investment?
2. What is the formula for continuous compounding, and how does it apply?
3. How do different interest rates impact the future value of an investment?
4. What is the future value of an investment if compounded monthly instead of annually?
5. How can one calculate the present value of a future amount?

**Tip:** Understanding the effects of compound interest is crucial for making informed investment decisions and planning for long-term financial goals.

Discover how to calculate the growth of a $100 investment over 10 years with a 5% interest rate using compound interest formulas. Understand the impact of compounding frequency on future investment value.

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