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Tiffany has taken out a loan with a stated interest rate of 8.145%. How much greater will Tiffany’s effective interest rate be if the interest is compounded weekly than if it is compounded semiannually?

a. 0.3340 percentage points
b. 0.1659 percentage points
c. 0.1681 percentage points
d. 0.1234 percentage points

Respuesta :

Answer:

c. 0.1681 percentage points

Step-by-step explanation:

We are given

annual interest rate is 8.145%

APR=8.145%

we can use formula

[tex]EAR=(1+\frac{APR}{m})^m-1[/tex]

where

APR is annual interest rate

m is number of periods

EAR is effective interest rate

Compounded weekly:

so,

n=52

APR=8.145%=0.08145

now, we can plug values

[tex]EAR=(1+\frac{0.08145}{52})^{52}-1[/tex]

[tex]EAR=0.08479[/tex]

so,

interest rate us 8.479%

Compounded semiannually:

so,

n=2

APR=8.145%=0.08145

now, we can plug values

[tex]EAR=(1+\frac{0.08145}{2})^{2}-1[/tex]

[tex]EAR=0.08311[/tex]

so,

interest rate us 8.311%

so, difference in interest rate is

=8.479% -8.311%

=0.168%

so,

c. 0.1681 percentage points

Answer:

0.1681 percentage points

Step-by-step explanation:

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