Question

Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. What is the total amount they will pay including interest?

$3,600.00

$3,357.16

$3,287.90

$3,364.86

Answer 1

\( 3,287.90 \to 3,287.90\left (1 + \dfrac{0.145}{12} \right )\to 3,287.90\left (1 + \dfrac{0.145}{12} \right ) - 1200\)

\(\to \left (3,287.90\left (1 + \dfrac{0.145}{12} \right ) - 1200\right) \dfrac{0.145}{12} \)

\(\to \left( \left (3,287.90\left (1 + \dfrac{0.145}{12} \right ) - 1200\right) \dfrac{0.145}{12} \right) - 1200 \)

maybe you don't follow that but there is no simple rubric. this is why spread sheets are so useful. once the debt falls below \(1200\), you then have to factor in the last payment being less than 1200.

none of this lends itself well to continuous maths, but it is simples in a spreadsheet where you have inbuilt binary stuff like "max()": yes, even in Windoze(!!), and especially in the M$ version.

fyi, i'd go with the last option.

Answer 2

@sillybilly123 Thanks!