Your mother-in-law is fretting about paying her mortgage. She refinanced her mortgage loan a while back, and now is thinking about refinancing again. You are going to help her evaluate her finances and decide if that makes sense. However, her record keeping is sketchy and you have less information than you might like to work with.

When she refinanced, money was easy, and she took out a $225,000 loan with payments based on fully amortizing the mortgage. She thinks she knows her payment, and her balance, but not how long the original term of mortgage was (only that it was probably something unusual, rather than the standard 30 year type) or the rate.

a. If her payment is $1,000 and the rate was originally 5.5% APR (compounded monthly), what is her remaining balance if she has 187 of the monthly payments left.

b. If she has made 200 monthly payments of $1,000 and has a remaining balance of $150,000, what must the APR have been when she took out the loan?

c. Suppose when she took out the initial loan for $225,000, the payment (not $1000; you need to calculate it) was based on an APR of 5.5% (compounded monthly) and full amortization over 30years of monthly payments.

Her monthly payment was determined based on those data. But, her lender has a new program in which new borrowers are allowed to skip their first three payments. The balance would continue to grow at the usual rate, and there would be no extra penalty for skipping the payments-the skipped payments just wouldn't contribute to the reduction of principal or payment of accruing interest (because they were skipped).

If she skipped those three payments, what will her remaining balance be after she makes the last of the360 regular payments?