Question

Madeline's credit card had an APR of 18.96% all of last year, and interest was compounded periodically throughout the year. Which of these statements accurately describes the effective interest rate of Madeline's credit card last year?

A. It was less than 18.96% whether interest was compounded daily or monthly.

B. It was greater than 18.96% whether interest was compounded daily or monthly.

C. It was greater than 18.96% if interest was compounded daily but not if interest was compounded monthly.

D. It was less than 18.96% if interest was compounded daily but not if interest was compounded monthly.

Answer 1

It was greater than 18.96 whether interest was compounded daily or monthly

Explanation:

Answer 2

Option B is correct, that is It was greater than 18.96% whether interest was compounded daily or monthly.

Explanation:

Given: APR of Madeline's Credit Card = 18.96 %

We need to find effective Interest rate of Madeline's credit card when compounded daily or compounded monthly.

Formula for Effective Interest is,

`Effective\:Rate=(1+(r)/(n))^n-1`

where, r is normal rate and n is number of periods.

When rate is compounded daily,

we have, r = 18.96% and n = 365

`Effective\:Rate=(1+((18.96)/(100))/(365))^(365)-1=20.87\,`%.

When rate is compounded monthly,

we have, r = 18.96% and n = 12

`Effective\:Rate=(1+((18.96)/(100))/(12))^(12)-1=20.7\,`%.

Therefore, Option B is correct, that is It was greater than 18.96% whether interest was compounded daily or monthly.