Question

You are considering two ways of financing a spring break vacation. You could put it on your credit card, at 17% APR, compounded monthly, or borrow the money from youe parents, who want an interest payment of 6% every six months. which is the lower rate? (Dont round intermediate steps to decimal places)

Answer 1

Answer: Parent's rate is lower.

Step-by-step explanation:

The lower rate will be the lower Effective Annual rate, the formula of which is;

`EAR = (1 + interest rate/compounding frequency) ^(compounding frequency) - 1`

Credit Card

`EAR = (1 + interest rate/compounding frequency) ^(compounding frequency) - 1`

`EAR = (1 + interest rate/compounding frequency) ^(compounding frequency) - 1\\= ( 1 + (0.17)/(12))^(12) - 1\\= 0.184`

= 18.4%

From your parents

`EAR = (1 + interest rate/compounding frequency) ^(compounding frequency) - 1\\= ( 1 + 0.07) ^(2) - 1\\= 0.1449`

= 14.5%

Parent's rate is lower.