1) You take out a 30-year $100,000 mortgage loan with an APR of 6% and monthly payments. In 12 payments (1year) you decide to sell your house and pay off the mortgage. What is the principal balance on the loan at the time you decide to pay it off?
2) To pay for your child's education, you wish to have accumulated $15,000 at the end of 15 years. To do this, you plan to deposit an equal amount into the bank at the end of each year. If the bank is willing to pay 6 percent compounded annually, how much must you deposit each year to obtain your goal?
3) Chase Bank pays 6.2% interest compounded semi-annually. Bank of America pays 6% interest, compounded monthly. Which bank offers the higher effective annual rate?
4) The Aggarwal Corporation needs to save $10M to retire a $10 million mortgage that matures in 10 years. To retire this mortgage, the company plans to put a fixed amount into an account at the end of the year for the 10 years, with the first payment occurring at the end of 1 year. The Aggarwal Corporation expects to earn 9% annually on the money in this account. What equal annual contribution must it make to this account to accumulate the $10 million in 10 years?
5) On December 31, Son-Nan Chen borrowed $100,000, agreeing to repay this sum in 20 equal end-of-year installments and 15 percent interest on the declining balance. How large must the annual payments be?
6) To buy a new house you must borrow $150,000. To do this you take out a $150,000, 30-year, 10 percent mortgage. Your mortgage payments, which are made at the end of each year (one payment each year), include both principal and 10 percent interest on the declining balance. How large will your annual payments be?
7) After examining the various personal loan rates available to you, you find that you can borrow funds from a finance company at 12 percent compounded monthly or from a bank at 13 percent compounded annually. Which alternative is more attractive?
8) The Kumar Corporation is planning on issuing bonds that pay no interest but can be converted into $1000 at maturity, 7 years from their purchase. To price these bonds competitively with other bonds of equal risk, it is determined that they should yield 10 percent, compounded annually. At what price should the Kumar Corporation sell these bonds?
9) How much do you have to deposit today so that beginning 11 years from now you can withdraw $10,000 a year for the next 5 years (periods 11 through 15) plus an additional amount of $20,000 in that last year (period 15)? Assume an interest rate of 6 percent.