To determine the interest rate per period (monthly interest rate) given an annual interest rate compounded monthly, follow these steps:
1. Identify the annual interest rate:
- The annual interest rate given is [tex]\(8.5\)[/tex]%.
2. Convert the annual interest rate to a decimal:
- Since percentage means per hundred, convert the annual interest rate from percentage to decimal form by dividing by [tex]\(100\)[/tex]:
[tex]\[
8.5\% = \frac{8.5}{100} = 0.085
\][/tex]
3. Convert the annual rate to a monthly rate:
- To get the monthly interest rate from the annual rate, divide by the number of months in a year (12):
[tex]\[
\text{Monthly Interest Rate} = \frac{0.085}{12}
\][/tex]
4. Perform the division:
- When you divide [tex]\(0.085\)[/tex] by [tex]\(12\)[/tex], you get:
[tex]\[
\frac{0.085}{12} \approx 0.007083333333333334
\][/tex]
Therefore, the value that should be used for [tex]\(i\)[/tex] in the formula is approximately [tex]\(0.0071\)[/tex].
So, from the choices provided:
a. 8.5
b. 0.71
c. 0.085
d. 0.0071
The best answer is:
D.
