Answer:
The annual interest rate of the loan was of 0.07 = 7%.
Explanation:
This is a simple interest problem.
The simple interest formula is given by:
![E = P*I*t](https://img.qammunity.org/2021/formulas/mathematics/college/rktontr3pu4u452xvr5dkqnhxmdwfw2bxf.png)
In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
.
In this problem, we have that:
4 years, so
![t = 4](https://img.qammunity.org/2021/formulas/mathematics/high-school/69ppk841uas0k864lhsk1z9wr53dr9z6eh.png)
Loan of 300, so
![P = 300](https://img.qammunity.org/2021/formulas/mathematics/high-school/80xlylofhevl1xktdd9tkd8gi24oohstyd.png)
Interest of 84, so
![E = 84](https://img.qammunity.org/2021/formulas/mathematics/high-school/b66t0o2gv69z324ymm9ykxkmni6ky3uiei.png)
We have to find I.
![E = P*I*t](https://img.qammunity.org/2021/formulas/mathematics/college/rktontr3pu4u452xvr5dkqnhxmdwfw2bxf.png)
![84 = 300*I*4](https://img.qammunity.org/2021/formulas/mathematics/high-school/jgxc1qjtcrxdktc7i3ck4wrkec0lkdcqp5.png)
![I = (84)/(300*4)](https://img.qammunity.org/2021/formulas/mathematics/high-school/j96pzg67ijmecdgalbmmcf5b5pbqpjjk3h.png)
![I = 0.07](https://img.qammunity.org/2021/formulas/mathematics/high-school/2stvunhnhmbcaw3yoq8kceehv1xc38h398.png)
The annual interest rate of the loan was of 0.07 = 7%.