Suppose you want to have $500,000 for retirement in 20 years. Your account earns 5% interest.How much interest will you earn?

To find out how much interest you will earn in 20 years, we can use the compound interest formula:

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

Where:
- $A$ is the future value of the investment/loan, including interest.
- $P$ is the principal amount (initial deposit or investment).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times that interest is compounded per year.
- $t$ is the time the money is invested or borrowed for, in years.

Since we are solving for the interest earned, we will first determine the initial principal required to reach $500,000 in 20 years. Assuming the interest is compounded annually (which means $n = 1$), the formula simplifies to:

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

In this case:
- $A = 500,000$
- $r = 0.05$ (5% annual interest rate)
- $t = 20$

Now, let's rearrange the formula to solve for $P$ (the initial principal):

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

Substituting the given values:

\[
P = \frac{500,000}{(1 + 0.05)^{20}}
\]

I'll calculate that for you.The initial principal you would need to invest is approximately $188,444.74.

To find the interest earned, we subtract the principal from the future value:

\[
\text{Interest Earned} = A - P
\]

Let's compute that next.The total interest earned over 20 years would be approximately $311,555.26.

Would you like more details or have any questions? 

Here are 5 related questions to deepen your understanding:
1. How would the interest earned change if the interest rate were 6%?
2. What if the investment was compounded quarterly instead of annually?
3. How much would you need to invest if you wanted to retire in 15 years with $500,000?
4. How does increasing the time period to 25 years affect the initial investment needed?
5. What happens to the interest if you make regular contributions to the account?

**Tip**: The frequency of compounding (annually, quarterly, monthly) significantly affects the total interest earned!

Suppose you want to have $500,000 for retirement in 20 years. Your account earns 5% interest. How much interest will you earn?

Discover how much interest you will earn with a $500,000 investment over 20 years at 5% interest, using the compound interest formula. Learn the breakdown of how interest accumulates and explore key concepts like exponential growth and compound interest. Suitable for high school students.

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