Question

credit card A offers an APR of 23.16% compounded monthly while credit card b offers and APR of 23.02% compounded daily. All else being equal which card offers the better deal for the consumer?.

Answer 1

Credit card A, because it's effective interest rate is about 0.09 LESS THAN that of credit card B.

Answer 2

Answer:

Credit card A offers better deal for the consumer.

Step-by-step explanation:

Since, the effective rate of interest is,

$r=(1+\frac{i}{n})^n-1$

Where, i is the stated annual rate,

n is the number of number of compounding periods,

For card A,

i = 23.16 % = 0.2316,

n = 12, ( 1 year = 12 months )

Thus, the effective interest rate,

$i_1=(1+\frac{0.2316}{12})^{12}-1$

$\implies i_1=0.257836782609\approx 0.25784$

While, For card B,

i = 23.02 % = 0.2302,

n = 365, ( 1 year = 12 months )

Thus, the effective interest rate,

$i_2=(1+\frac{0.2302}{365})^{365}-1$

$\implies i_2=0.258760414464\approx 0.25876$

Since,  0.25784 < 0.25876

$\implies i_1< i_2$

Hence, credit card A offers better deal for the consumer.