Question

You are considering two ways of financing a spring break vacation. You could put it on your credit​ card, at 14 %14% ​APR, compounded​ monthly, or borrow the money from your​ parents, who want an interest payment of 8 %8% every six months. Which is the lower​ rate? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

Credit card is at lower rate at 14.93% interest rate

Step-by-step explanation:

Data provided in the question:

APR on credit card = 14% compounded monthly

Interest rate from parents = 8% compounded every six months

Now,

Annual interest rate = (1 + r )ⁿ - 1

Here,

r is the interest rate for the period

n is the total period

Thus,

For the credit card

since compounded monthly

Interest rate per month, r = 14% ÷ 12 = 1.167% = 0.01167

Number of periods, n = 12

Therefore,

Annual interest = (1 + 0.01167 )¹² - 1 = 0.1493

or

= 0.1493 × 100% = 14.93%

For borrowing from parents

since compounded every six months

Number of periods, n = 12 months ÷ 6 = 2

Interest rate , r = 8% = 0.08

Therefore,

Annual interest = (1 + 0.08 )² - 1 = 0.1664

or

= 0.1664× 100% = 16.64%

Credit card is at lower rate at 14.93% interest rate