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

Credit card A offers better deal for the consumer.

Explanation:

Since, the effective rate of interest is,

`r=(1+(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+(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+(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.