Answer :
To find the annual interest rate based on a two-week interest rate of 7.00%, follow these steps:
1. Identify the given data:
- Two-week interest rate = 7.00%
2. Determine the number of two-week periods in a year:
- There are 52 weeks in a year.
- Since each period is two weeks, the number of two-week periods in a year is [tex]\( \frac{52}{2} = 26 \)[/tex].
3. Calculate the annual interest rate:
- The formula for calculating the annual interest rate [tex]\( A \)[/tex] from the periodic interest rate [tex]\( R \)[/tex] is given by:
[tex]\[ A = (1 + \frac{R}{100})^{n} - 1 \][/tex]
where [tex]\( n \)[/tex] is the number of periods per year.
Substituting the given values:
[tex]\[ R = 7.00 \text{ percent} \quad \text{and} \quad n = 26 \][/tex]
[tex]\[ A = (1 + \frac{7.00}{100})^{26} - 1 \][/tex]
4. Calculate the interest rate using the provided numbers:
[tex]\[ A = (1 + 0.07)^{26} - 1 \approx 4.807352924931501 \][/tex]
5. Convert the annual interest rate to a percentage:
- Multiply the result by 100 to convert it to percentage form:
[tex]\[ \text{Annual interest rate} = 4.807352924931501 \times 100 \approx 480.74 \text{ percent} \][/tex]
When rounded to two decimal places, the annual interest rate is:
[tex]\[ \boxed{480.74 \%} \][/tex]
1. Identify the given data:
- Two-week interest rate = 7.00%
2. Determine the number of two-week periods in a year:
- There are 52 weeks in a year.
- Since each period is two weeks, the number of two-week periods in a year is [tex]\( \frac{52}{2} = 26 \)[/tex].
3. Calculate the annual interest rate:
- The formula for calculating the annual interest rate [tex]\( A \)[/tex] from the periodic interest rate [tex]\( R \)[/tex] is given by:
[tex]\[ A = (1 + \frac{R}{100})^{n} - 1 \][/tex]
where [tex]\( n \)[/tex] is the number of periods per year.
Substituting the given values:
[tex]\[ R = 7.00 \text{ percent} \quad \text{and} \quad n = 26 \][/tex]
[tex]\[ A = (1 + \frac{7.00}{100})^{26} - 1 \][/tex]
4. Calculate the interest rate using the provided numbers:
[tex]\[ A = (1 + 0.07)^{26} - 1 \approx 4.807352924931501 \][/tex]
5. Convert the annual interest rate to a percentage:
- Multiply the result by 100 to convert it to percentage form:
[tex]\[ \text{Annual interest rate} = 4.807352924931501 \times 100 \approx 480.74 \text{ percent} \][/tex]
When rounded to two decimal places, the annual interest rate is:
[tex]\[ \boxed{480.74 \%} \][/tex]
