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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 please select the best answer from the choices provided a b c d

Sagot :

Tiffany's effective interest is compounded weekly is 0.1604% greater than the compounded semiannually.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Given,

The interest rate i= 8.145%

Number of weeks in an year n= 52

We know,

Effective interest rate =[tex](1+\frac{i}{n})^{n}-1[/tex]

Substitute the values

[tex]R_{1}=(1+\frac{0.08145}{52})^{52}-1\\ R_{1}= 0.084789[/tex]

Case 2

Compounded semiannually

[tex]R_{2}=(1+\frac{0.08145}{2})^{2}-1\\ R_{2}=0.083108[/tex]

The difference is

[tex]R_{1}-R_{2}= 0.084789-0.083185[/tex]

=0.001604

=0.1604%

Hence, the Tiffany's effective interest is compounded weekly is 0.1604% greater than the compounded semiannually

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