Sure, let's solve this step by step.
1. Understanding the Problem:
- We need to find the monthly interest rate per period, denoted as [tex]\(i\)[/tex], for an annual interest rate of [tex]\(8.5\%\)[/tex].
2. Converting Annual Interest Rate to Monthly Interest Rate:
- The annual interest rate given is [tex]\(8.5\%\)[/tex].
- Interest rates are typically expressed as a percentage, so [tex]\(8.5\%\)[/tex] means [tex]\(8.5\)[/tex] per [tex]\(100\)[/tex], mathematically written as [tex]\(8.5/100\)[/tex].
3. Monthly Interest Rate:
- To convert an annual interest rate to a monthly interest rate, we need to divide by [tex]\(12\)[/tex], since there are [tex]\(12\)[/tex] months in a year.
- So, the monthly interest rate is:
[tex]\[
\text{Monthly interest rate} = \frac{8.5}{12}/100
\][/tex]
- Simplifying the division:
[tex]\[
\text{Monthly interest rate} = \frac{8.5}{1200}
\][/tex]
4. Numerical Value of Monthly Interest Rate:
- Evaluating the fraction [tex]\(\frac{8.5}{1200}\)[/tex] results in approximately [tex]\(0.007083333333333334\)[/tex].
5. Selecting the Best Answer:
- Comparing this result with the choices provided,
[tex]\[
\text{Choices:}
\][/tex]
- (a) [tex]\(8.5\)[/tex]
- (b) [tex]\(0.71\)[/tex]
- (c) [tex]\(0.085\)[/tex]
- (d) [tex]\(0.0071\)[/tex]
- The closest and most accurate value corresponding to our obtained result [tex]\(0.007083333333333334\)[/tex] is:
[tex]\[
d. \quad 0.0071
\][/tex]
Thus, the best answer is:
[tex]\[
\boxed{0.0071}
\][/tex]
