The simple interest formula is given to be:
![I=(PRT)/(100)](https://img.qammunity.org/2023/formulas/mathematics/college/ow8jstobgep8k2tjmvzz2thz894ax97bk5.png)
where P is the principal, R is the interest rate, and T is the time in years.
From the given question, the following parameters are provided:
![\begin{gathered} P=900 \\ R=14 \\ T=9\text{ years and }3\text{ months}=9.25\text{ years} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/xyftt365oa4wwoo3yzjshorzx0pft4792u.png)
Therefore, the interest after 9 years and 3 months will be:
![\begin{gathered} I=(900*14*9.25)/(100) \\ I=1165.50 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/tm6x2vd9jgixrkqi846zyelvqe4zy1vdcs.png)
Hence, the value of the investment will be:
![\Rightarrow P+I=900+1165.50=2065.50](https://img.qammunity.org/2023/formulas/mathematics/college/xd9jdl9z75nvaku2ndgo8n47gn6schfwyi.png)
The value of the investment will be R2065.50.