Answer: 9 months.
Step-by-step explanation:
Simple interest = Principal x rate(in decimal) x Time(in years)
Given: Principal = $15,000 , rate = [tex]5\dfrac12\%=\dfrac{11}{2}\%= 5.5\%= 0.055[/tex]
Interest = $618.75
let t= time
Then,
[tex]618.75=15000\times 0.055\times t\\\\\Rightarrow\ t=\dfrac{618.75}{15000\times0.055}\\\\\Rightarrow\ t= 0.75\ or\ t=\dfrac34\ year[/tex]
1 year =12 months
[tex]\dfrac34\ year=\dfrac34\times12 = 9\ months[/tex]
Hence, it will take 9 months.
