The problem states that the interest is compounded monthly. For uniformity, we convert 10 years to months. This is equivalent to 120 months.
The equation would be
[tex]F=P (1+i)^{n} [/tex]
where F is the future worth = $4,573.23
P is the present worth = $4,000
n is the number of periods = 120 months
[tex]4,573.23= 4,000(1+i)^{120}[/tex]
[tex] \frac{4573.23}{4000}= (1+i)^{120} [/tex]
[tex]1+i = \sqrt[20]{1.1433075} [/tex]
[tex]i = 1.00672-1[/tex]
[tex]i = 0.00672 \ (nominal \ rate)[/tex]
To convert to effective rate
[tex] i_{eff} =(1+ \frac{i}{m} )^{m}-1 [/tex]
where m is the number of periods in a year. There are 120 month in a year.
[tex] i_{eff} =(1+ \frac{0.00672}{120} )^{120}-1 [/tex]
[tex] i_{eff} = 0.00674[/tex]
or,
The annual interest rate would be 0.67%
