Caleb has an offer from a credit card issuer for 0% APR for the first 30 days and 17.68% APR afterwards, compounded daily. What effective interest rate is Caleb being offered? 17.61% 19.19% 17.68% 19.33%

Solution:- Answer is 19.33%Annual percentage rate (APR) is the yearly rate for a price which have to pay for borrowing money through credit card.Here Caleb has an offer from a credit card issue for i=0% APR for the first 30 days.now, effective interest rate for n= 30 days  =[tex]r=(1+\frac{i}{n} )^n-1\\\Rightarrow\ r=(1+\frac{0}{30} )^{30}-1\\\Rightarrow\ r=(1+0)^{30}-1=1-1=0[/tex]After 30 days APR =17.68%=0.1768n=365-30=335 daysnow the effective interest rate for n=335 days =[tex]r=(1+\frac{i}{n} )^n-1\\\Rightarrow\ r=(1+\frac{0.1789}{335} )^{335}-1\\\Rightarrow\ r=(1+0.000527)^{335}-1=(1.000527)^{335}-1=1.1933-1=0.1933[/tex]=19.33%So the effective interest rate for 365 days =0+19.33% =19.33%So fourth option is correct.