Question

You take out a cash advance of $2,790.00 on a credit card with a 3.5% cash advance fee and a 13.5% APR. What is the amount due by the end of the month?

$3,277.48

$2,920.14

$2,887.65

$2,821.39

Answer 1

@sillybilly123 if it wouldn't be too much trouble would you mind taking a look at this?

Answer 2

Three components to the end of month balance

- the principal advanced = 2,790

- the cash advance fee = 3.5% * 2,790

- the APR (cost of borrowing).

For APR, you need to convert the 13.5% APR into a monthly rate \(r\)

For a nominal APR, more common in the US, it's just \(r = \dfrac{13.5}{12} = 1.125 \%\)

More sophisticated models us an effective APR which needs to be de-compounded:

\((1 + r)^{12} = 1 + APR \implies r = (1 + APR)^{1/12} - 1 = 1.06 \%\)

Using the nominal APR, the cost due to APR is: 2,790 * 1.125 %

Adding it all up:

2,790 + 3.5 % * 2,790 + 2,790 * 1.125 % = 2,790 ( 1 + 3.5 % + 1.125 %) = 2,919.04