Question

A credit card had an APR of 33.01% all of last year and compounded interest

Answer 1

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,

$\text{APR}=(1+\dfrac{r}{n})^n-1$

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,

$\text{APR}=(1+\dfrac{0.3301}{365})^{365}-1$

$\text{APR}=(1+000904)^{365}-1$

$\text{APR}=(1.000904)^{365}-1$

$\text{APR}=1.39089-1$

$\text{APR}=0.39089$

Into percentage,  

$\text{APR}=0.39089\times 100$

$\text{APR}=39.089\%$

$\text{APR}\approx 39.09\%$

Therefore, the credit card's effective interest rate last year is 39.09%.

So, Option D is correct.