Answer:
5 months
ROI = 3.75 %
Step-by-step explanation:
Since,
The simple interest formula,
![I=P\times r\times t](https://tex.z-dn.net/?f=I%3DP%5Ctimes%20r%5Ctimes%20t)
Where,
P = Principal amount,
r = rate per period ( in decimal )
t = number of periods,
Here, P = 800, r = 9% = 0.09,
If A is the future amount,
We have, A = 830
I = A - P = 830 - 800 = 30
By substituting the values in the above formula,
![30=800\times 0.09\times t](https://tex.z-dn.net/?f=30%3D800%5Ctimes%200.09%5Ctimes%20t)
![30=72t](https://tex.z-dn.net/?f=30%3D72t)
![\implies t =\frac{30}{72}=\frac{5}{12}](https://tex.z-dn.net/?f=%5Cimplies%20t%20%3D%5Cfrac%7B30%7D%7B72%7D%3D%5Cfrac%7B5%7D%7B12%7D)
Hence, it will take 5 months. ( 1 year = 12 months )
Now,
![\text{Return on investment }=\frac{I}{P}\times 100](https://tex.z-dn.net/?f=%5Ctext%7BReturn%20on%20investment%20%7D%3D%5Cfrac%7BI%7D%7BP%7D%5Ctimes%20100)
![=\frac{30}{800}\times 100](https://tex.z-dn.net/?f=%3D%5Cfrac%7B30%7D%7B800%7D%5Ctimes%20100)
![=3.75\%](https://tex.z-dn.net/?f=%3D3.75%5C%25)