Respuesta :
The correct option for Tiffany to be effective at the interest rates both quarterly and semiannually is approx to 0. 1681 percentage points.
Effective Interest Rate:
We have given with the stated interest rate = 8.145%.
The formula for effective interest rate,
[tex]r=(1+\frac{i}{n})^{n}-1[/tex]
Where, r = effective interest rate,
i = stated interest rate,
n = number of compounding periods,
Tiffany's effective interest rate:
Tiffany's effective interest rate if the interest is compounded weekly, Stated interest rate, i = 8.145%,
Number of compounding periods, n = 1 week = 1,
[tex]r=(1+\frac{i}{n})^{n}-1\\r=(1+\frac{0.08145}{1})^{1}-1\\r=0.08145\\r=8.145\%[/tex]
Number of compounding periods, n = 1 year = 52 weeks = 52,
[tex]r=(1+\frac{i}{n})^{n}-1\\r=(1+\frac{0.08145}{52})^{52}-1\\r=0.084789\\r=8.478\%[/tex]
Tiffany's effective interest rate be if the interest is compounded semiannually,
Stated interest rate, i = 8.145%,
Number of compounding periods, n = for half year = 1,
[tex]r=(1+\frac{i}{n})^{n}-1\\r=(1+\frac{0.08145}{1})^{1}-1\\r=0.08145\\r=8.145\%[/tex]
Number of compounding periods, n = 2 semiannually = 2,
[tex]r=(1+\frac{i}{n})^{n}-1\\r=(1+\frac{0.08145}{2})^{2}-1\\r=0.0831\\r=8.31\%[/tex]
Thus, the effective interest rate will remain unchanged for the first week and one semiannually, but will undoubtedly alter after a year.
As a result, Tiffany's effective interest rate will be if interest is compounded weekly rather than semiannually.
As a result, option c, 0.1689, is right.
Learn more about the effective annual rate here:
https://brainly.com/question/24523385
