3. A couple wish to buy a house for $520,000. They have saved enough for a 20% down payment, and will finance the remainder with a 30-year fixed rate mortgage. Their budget allows for a monthly payment of $2,100. (For this problem, ignore agents fees, closing costs, taxes, and insurance.) Show all work.

(a) What is the largest annual effective interest rate for their loan that will allow them to afford this purchase? Give your answer as a percentage correct to 3 decimal places.

(b) Suppose they take out a loan at 4.125% annual effective interest, and make monthly payments of $2,100. What is the outstanding balance on the loan after 10 years of payments?