Using simple interest, it is found that the rate is of 0.1205 = 12.05%.
The amount of money earned in simple interest after t years is given by:
[tex]I = Pit[/tex]
In which:
- P is the principal, which is the initial deposit.
- r is the interest rate, as a decimal.
In this problem, we have that:
- The interest earned is [tex]I = 160.67[/tex]
- The principal is [tex]P = 2000[/tex].
- The time is of 8 months, it should be in years, hence [tex]t = \frac{8}{12} = \frac{2}{3}[/tex]
Then:
[tex]I = Pit[/tex]
[tex]160.67 = 2000\frac{2}{3}i[/tex]
[tex]i = \frac{160.67 \times 3}{4000}[/tex]
[tex]i = 0.1205[/tex]
The rate is of 0.1205 = 12.05%.
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