Rodyon Raskolnikov borrowed $500,000 to buy a house as an investment. The rate was 5.147% p.a. compounded semi-annually. The terms of the loan stipulated two payments per month with a term of 25 years. The first payment was to occur half a month after taking out the loan.
a) What was the principal portion of the 245th repayment?
b) Rodyon knew that the bulk of the repayment would consist of interest during the early days of repaying the loan and that the interest portion would get less and less as time passed. At which payment would the interest portion of the payment first drop; to less than half the repayment?