Answer:
Interest rate = 3%
Step-by-step solution:
The formula to find the amount for the principal P, after n years with annual rate of interest r% compounded quarterly is:
[tex]A=P(1+\frac{r}{4} )^{4n}[/tex]
Here, P = 4000, A = 5234.58 and n = 9
Therefore,
[tex]5234.58=4000(1+\frac{r}{4} )^{4(9)}[/tex]
[tex]\frac{5234.58}{4000} = (1+\frac{r}{4} )^{36}[/tex]
[tex]1.308645 = (1+\frac{r}{4} )^{36}[/tex]
[tex]1+\frac{r}{4} =1.308645 ^{\frac{1}{36} }[/tex]
[tex]1+\frac{r}{4} =1.0075[/tex]
[tex]\frac{r}{4} =1.0075-1[/tex]
= 0.0075
r = 0.0075 × 4 = 0.03
= 3%
