We have to calculate the annual interest rate.
We know:
• Future value (FV): 35,349.62
,
• Present value (PV): 6,000
,
• Period: (n): 15 years
,
• Number of subperiods (m): 4 periods per year (quarterly)
We can relate this values with the equation:
[tex]FV=PV(1+\frac{r}{m})^{n\cdot m}[/tex]
We can replace with the known values and calculate r as:
[tex]\begin{gathered} 35349.62=6000(1+\frac{r}{4})^{15*4} \\ \frac{35349.62}{6000}=(1+\frac{r}{4})^{60} \\ \sqrt[60]{5.89160}=1+\frac{r}{4} \\ 1.03-1=\frac{r}{4} \\ 0.03=\frac{r}{4} \\ r=4*0.03 \\ r=0.12 \end{gathered}[/tex]
The annual rate is r = 0.12, which expressed in percentage corresponds to 12%.
Answer: the annual rate is 12%
