In: Finance
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 your parents, who want an interest payment of 10% every six months. Which is the lower rate? (Note: Be careful not to round any intermediate steps less than six decimal places.) The effective annual rate for your credit card is nothing %. (Round to two decimal places.)
The effective annual rate for the credit card is calculated
as:
Effective annual rate =[(1+Annual percentage rate/Number of
compounding periods)^(Number of compounding periods)]-1
For the credit card, annual percentage rate (APR)=17% compounded
monthly.
So, the number of compounding periods=12 per year
We will have effective annual rate=[(1+17%/12)^12]-1
=[(1+0.17/12)^12]-1
=[(1.014166667)^12]-1
=[1.183891733]-1
=0.183891733
This will be equal to 18.39% (rounded up to two decimal
places)
The effective annual rate for the credit card=18.39%
The effective annual rate for the loan from parents is calculated as:
Rate of interest=10%
We won't divide the interest rate by 2 because we are already
provided with the six-month rate. This interest rate is not the
annual rate that is compounded semiannually.
Compounding periods=2 (in a year)
So, putting the value in the equation of effective annual rate, we
get
So, effective annual rate= [(1+10%)^2]-1
=[(1.10)^2]-1
=[1.21]-1
=.21
This will be equal to 21%
So, the effective annual rate for the loan from parents=21%
The effective annual rate of the credit card is lower and is 18.39%.