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