Question

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?

Answer 1

Answer: 0.1681 percentage point

Step-by-step explanation:

Here the stated interest rate = 8.145% = 0.08145

If the interest is calculated weekly,

In one year number of weeks= 52,

Thus, the effective interest rate in that case,

$r_1 = (1+\frac{0.08145}{52})^{52} - 1$

⇒ $r_1 = 0.0847898451$

Now, If the interest is calculated semiannually,

In one year number of half years in one year = 2

Thus, the effective interest in that case,

$r_2 = (1+\frac{0.08145}{2})^{2} - 1$

⇒ $r_2 = 0.08310852562$

Since,  $r_1-r_2 = 0.0847898451-0.0831851562=0.00168131947=0.168131947\% \approx 0.1681\%$

Thus, Tiffany's effective interest rate is 0.1681 percentage point greater when the interest is calculated compound weekly than when the interest is calculated compound weekly.

Answer 2

20.135% just think about it really its easy