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? 1…

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asked Mar 18, 2019 88.7k views

2 Answers

Alex Yu · Answer 1 · 2019-03-22T23:37:10+0000

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

=
$r=(1+(i)/(n) )^n-1\\\Rightarrow\ r=(1+(0)/(30) )^(30)-1\\\Rightarrow\ r=(1+0)^(30)-1=1-1=0$

After 30 days APR =17.68%=0.1768

n=365-30=335 days

now the effective interest rate for n=335 days

=
$r=(1+(i)/(n) )^n-1\\\Rightarrow\ r=(1+(0.1789)/(335) )^(335)-1\\\Rightarrow\ r=(1+0.000527)^(335)-1=(1.000527)^(335)-1=1.1933-1=0.1933$

=19.33%

So the effective interest rate for 365 days =0+19.33% =19.33%

So fourth option is correct.