Answer:
Option D - 39.09%
Step-by-step explanation:
Given : A credit card had an APR of 33.01% all of last year and compounded interest daily.
To find : What was the credit card's effective interest rate last year?
Solution :
Effective annual rate formula is given by,
[tex]\text{APR}=(1+\dfrac{r}{n})^n-1[/tex]
where, r is the interest rate i.e. r=33.01%=0.3301
n is the number of time period for which interest is compounded daily i.e. n=365.
Substitute in the formula,
[tex]\text{APR}=(1+\dfrac{0.3301}{365})^{365}-1[/tex]
[tex]\text{APR}=(1+000904)^{365}-1[/tex]
[tex]\text{APR}=(1.000904)^{365}-1[/tex]
[tex]\text{APR}=1.39089-1[/tex]
[tex]\text{APR}=0.39089[/tex]
Into percentage,
[tex]\text{APR}=0.39089\times 100[/tex]
[tex]\text{APR}=39.089\%[/tex]
[tex]\text{APR}\approx 39.09\%[/tex]
Therefore, the credit card's effective interest rate last year is 39.09%.
So, Option D is correct.
