Answer:
![r=3.8\%](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8ik26facnlru7zibojfyrmnx96jyws2ilv.png)
Explanation:
we know that
The simple interest formula is equal to
![I=P(rt)](https://img.qammunity.org/2020/formulas/mathematics/college/mobnh6zyv5me8p7h5kezfv406oss475cu5.png)
where
I is the interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
![t=(91/365)\ years\\ P=\$2,400\\ I=\$22.74\\r=?](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jxoxj1l0qap4xf5quwmjdijend3xdnd1gd.png)
substitute in the formula above
![22.74=2,400(91/365)r](https://img.qammunity.org/2020/formulas/mathematics/middle-school/pipctwfqu69vuvskjd3ovt2tg8kn79h59t.png)
![22.74*365=2,400(91)r](https://img.qammunity.org/2020/formulas/mathematics/middle-school/lwohl39ynzfwhm5755fngxsxo2fmrezfrz.png)
![r=22.74*365/[2,400(91)]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/rp3ahdww0fe9of0bauwexkd4oqkvd6nuz9.png)
![r=0.038](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ebby5fjjax6t0vr92sybumcmkfe3qxqm1u.png)
![r=3.8\%](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8ik26facnlru7zibojfyrmnx96jyws2ilv.png)