Question

The average long-term mutual fund in 2023 earns 6.19% annually. Write an exponential equation to show the total money, y, that you would have if you invested $1000 for x years.The average long-term mutual fund in 2023 earns 6.19% annually. Write an exponential equation to show the total money, y, that you would have if you invested $1000 for x years.

Answer 1

The equation
`\(y = 1000 * (1 + 0.0619)^x\)` calculates the total money
`\(y\)` after
`\(x\)` years with $1000 invested at 6.19% annual interest, yielding approximately $1343.90 after 5 years.

To solve the equation
`\( y = 1000 * (1 + 0.0619)^x \)` let's say we want to find the total amount after 5 years.

`\[ y = 1000 * (1 + 0.0619)^5 \]`

First, calculate
`\( (1 + 0.0619) \)`:

`\[ 1 + 0.0619 = 1.0619 \]`

Now, raise
`\( 1.0619 \)` to the power of 5:

`\[ 1.0619^5 \approx 1.3439 \]`

Now, multiply
`\( 1000 \)` by
`\( 1.3439 \)` to find the total amount after 5 years:

`\[ y = 1000 * 1.3439 \]`

`\[ y \approx 1343.9 \]`

So, after 5 years, the total amount of money accumulated would be approximately $1343.90 if you invested $1000 at an annual interest rate of 6.19%.