Joy is taking out a car loan which she will pay back with interest.which option will require her to pay the lowest amount in interest?

The answer is "annual compounding".

With whatever is left of the compoundings she should pay more cash. With a semi-yearly rate she wil need to pay right around 1000 dollars more than in an anual intensifying. With a quarterly period she should pay nearly an indistinguishable sum from a semi-yearly period. Presently with a monthly time span she would need to pay just about 2000 dollars of interest.