To find the exact value of [tex]\( i \)[/tex] in the future value ordinary annuity formula:
[tex]\[ FV = P \left( \frac{(1+i)^x - 1}{i} \right) \][/tex]
we need to convert the given annual interest rate into a monthly interest rate, as the interest is compounded monthly.
Given:
- Annual interest rate ([tex]\( r \)[/tex]) = [tex]\( 2.1\% \)[/tex]
Step-by-step explanation:
1. Convert the annual interest rate to a decimal:
[tex]\[ r = \frac{2.1}{100} = 0.021 \][/tex]
2. Determine the monthly interest rate:
Since the interest rate is compounded monthly, we need to divide the annual rate by 12 (the number of months in a year):
[tex]\[ i = \frac{0.021}{12} \][/tex]
So the exact value of [tex]\( i \)[/tex] is:
[tex]\[ i = 0.00175 \][/tex]
Thus, the correct answer is:
c. [tex]\(\frac{0.021}{12}\)[/tex]
