Question

Find the annual interest rate. (Round your answer to the nearest whole number.)

Answer 1

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:

`FV=PV(1+(r)/(m))^(n\cdot m)`

We can replace with the known values and calculate r as:

`\begin{gathered} 35349.62=6000(1+(r)/(4))^(15*4) \\ (35349.62)/(6000)=(1+(r)/(4))^(60) \\ \sqrt[60]{5.89160}=1+(r)/(4) \\ 1.03-1=(r)/(4) \\ 0.03=(r)/(4) \\ r=4*0.03 \\ r=0.12 \end{gathered}`

The annual rate is r = 0.12, which expressed in percentage corresponds to 12%.

Answer: the annual rate is 12%