The annual interest rate is: 3.5%.
The formula for simple interest is:
![\[ I = P \cdot r \cdot t \]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/28vy2hxsp2dme72hksx7fz103q52g39a95.png)
where:
- I is the interest earned,
- P is the principal amount (initial investment),
- r is the annual interest rate, and
- t is the time in years.
In this case:
- P = $6000,
- I = $1050,
- t = 5 years.
We can rearrange the formula to solve for the interest rate r:
![\[ r = (I)/(P \cdot t) \]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/aaermllq67597fz7lq23fso4gwae3la8hw.png)
Substitute the given values:
![\[ r = ($1050)/($6000 \cdot 5) \]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/s0jq4y4xgdvrv8j34zbtikxo6dcsxsbxja.png)
Calculate:
![\[ r = ($1050)/($30000) \]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/fstlttg424nn3bhvo0m8a1f32hplwwia3i.png)
![\[ r = 0.035 \]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/oepmfn6nkrmwp3k6f33cqcmy3tnnay8q67.png)
Now, convert the decimal to a percentage by multiplying by 100:
![\[ r = 0.035 * 100 \]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/wysx85s71iw4zjr3hxso2ye69c48o0yld9.png)
![\[ r = 3.5\% \]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/2jnwc30aspzmt8mvhctvynjhq3b59bpqyv.png)
Therefore, the annual interest rate is 3.5%.