To determine the correct value for [tex]\( r \)[/tex] in the monthly payment formula [tex]\( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \)[/tex], given an annual interest rate of [tex]\( 6.9\% \)[/tex]:
1. Understand the Given Interest Rate:
The given interest rate is [tex]\( 6.9\% \)[/tex]. This is an annual interest rate.
2. Convert the Interest Rate from Percent to Decimal:
To use this rate in the monthly payment formula, we need to convert the percentage to a decimal form. This is done by dividing the percentage by 100:
[tex]\[
r = \frac{6.9}{100}
\][/tex]
3. Perform the Conversion:
Carrying out the division,
[tex]\[
r = \frac{6.9}{100} = 0.069
\][/tex]
4. Identify the Correct Choice:
Comparing this result with the given options:
- A. 0.00575
- B. 0.0069
- C. 0.575
- D. 6.9
The correct value for [tex]\( r \)[/tex], which matches our result of [tex]\( 0.069 \)[/tex], is not listed as an exact match. However, the closest match in decimal form is option B (0.0069), but since it is not entirely correct, the nearest suitable value is none other than the closest in form with proper scaling.
Therefore, based on our conversion, the value of [tex]\( r \)[/tex] for an interest rate of [tex]\( 6.9\% \)[/tex] is [tex]\( 0.069 \)[/tex]. The correct answer selection would be aligned with a refined understanding or decimal verification.
