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.)

Credit card is at lower rate at 14.93% interest rate

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