The formula for the simple interest is:
[tex]A=A_0\cdot(1+n\cdot r).[/tex]Where:
• A is the final amount of money after n years,
,• A0 is the initial amount of money,
• r is the interest rate.
In this problem, we have.
• A = $1100,
,• A0 = $1070,
,• n = 1.5 years,
,• r = ?.
Replacing the data of the problem in the equation above, we have:
[tex]\text{ \$1100 }=\text{ \$1070}(1+1.5\cdot r).[/tex]Solving the last equation for r, we get:
[tex]\begin{gathered} \frac{\text{ \$1100}}{\text{ \$1070}}=1+1.5r, \\ \frac{1100}{1070}-1=1.5r, \\ r=\frac{1}{1.5}\cdot(\frac{1100}{1070}-1), \\ r\cong0.0187=1.87\%. \end{gathered}[/tex]Answer
The interest rate was charged at 1.87%.
