You are offered three different loans all at the same interest rate, but they all different payment frequencies. The payments are due monthly, quarterly and semi-monthly respectively. Which loan has the lowest annual cost?

You are offered three different loans all at the same interest rate, but they all different payment frequencies. The payments are due monthly, quarterly and semi-monthly respectively. Which loan has the lowest annual cost?
The monthly because the principal amount is reduced monthly. The lower the principal the lower the interest charges. The loan is amortized at a faster rate by paying monthly. To balance the cost out over the same term you will incur a higher payment otherwise it will take longer to pay the loan off and thus the loan will cost more.

Except that semi-monthly means twice a month, which is more often than monthly. :-) (Though I do have to wonder if that was a typo, because it just seems out of place or something.)