1. You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly 18.5 years old, and you have just made a payment. If the interest rate on the mortgage is 7.75% (APR with semi-annual compounding), how much cash will you have from the sale once you pay off the mortgage?
2. You have just purchased a home and taken out a $500,000 mortgage. The mortgage has a 30-year term with monthly payments and an APR (with semi-annual compounding) of 6.5%. How much will you pay in interest, and how much will you pay in principal, during the 20th year (i.e., between 19 and 20 years from now)?
3. You have some extra cash this month and are considering putting it toward your car loan. Your interest rate 7%; your loan payments are $600 per month; and you have 36 months left on your loan. If you pay an additional $1000 with your next regular $600 payment (due in one month), how much will it reduce the amount of time left to pay off your loan?