Question

A credit card issuer offers an APR of 15.83% and compounds interest daily.

Which is it most likely to advertise, its APR or its effective interest rate?
A. Its APR, because it's 1.32% greater than its effective interest rate.
B. Its effective interest rate, because it's 1.32% less than its APR.

C. Its APR, because it's 1.32% less than its effective interest rate.
EST

D. Its effective interest rate, because it's 1.32% greater than its APR.
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Answer 1

C. Its APR, because it's less than its effective interest rate.

Explanation:

The interest rate determines the money you must pay on the outstanding balance on the credit card.

The credit card company would advertise the lowest numbers it could truthfully use.

The APR is 15.83 %.

The formula for the effective interest rate is

`i = \left (1 + (r)/(n) \right )^(n) - 1`

where the interest rates are expressed as decimals.

If the APR is 15.83% and the interest is compounded daily,

`\begin{array}{rcl}i & = & \left (1 + (0.1583)/(365) \right )^(365) -1\\\\ & = & (1 + 0.0004337)^(365) -1\\ & = & (1.0004337)^(365) -1\\ & = & 1.1715 - 1\\& = & 0.1715\\& = & 17.15 \%\\\end{array}\\\text{The effective interest rate is $\mathbf{17.15 \%}$}`

The APR is less than the effective interest rate, so that's what the company would advertise.