Given the simple interest formula
[tex]\begin{gathered} I=\text{ Prt} \\ \text{Where I=Interest; P=Principal; r=Rate and t=Time} \end{gathered}[/tex]From the question, the money deposited is the Principal P=$16,000;
The earned interest I=$4000;
The simple interest rate, r= 6%;
and the time period in years, t= unknown
To find the time unknown time, we substitute for I, P, and r in the formula given. This will give
[tex]\begin{gathered} I=\text{ Prt} \\ 4000=16000\times\frac{6}{100}\times t \\ 4000=\frac{16000\times6\times t}{100} \\ 4000=\frac{96000t}{100} \\ 4000=960t \\ t=\frac{4000}{960} \\ t=\frac{50}{12}\text{years} \end{gathered}[/tex]Since the time given in the options are in months, we will convert time gotten to months
[tex]\begin{gathered} \text{Convert }\frac{50}{12}\text{years to months} \\ \text{Note 1 year=12months} \\ \text{Therefore, }\frac{50}{12}\text{years}=\frac{50}{12}\times12months \\ =50\text{months} \end{gathered}[/tex]Therefore, the time period in months is 50months
