You have a loan outstanding. It requires making 4 annual payments at the end of the next

4 years of $4,000 each. Your bank has offered to allow you to skip making the next 3

payments in lieu of making one large payment at the end of theloan's term in

4 years. If the interest rate on the loan is 9.75%, what final payment will the bank require you to make so that it is indifferent between the two forms ofpayment?

When you purchased yourhouse, you took out a30-year annual-payment mortgage with an interest rate of 7% per year. The annual payment on the mortgage is 16,803. You have just made a payment and have now decided to pay the mortgage off by repaying the outstanding balance.

a. What is the payoff amount if you have lived in the house for 11 years(so there are 19 years left on themortgage)?

b. What is the payoff amount if you have lived in the house for 24 years(so there are 6 years left on themortgage)?

c. What is the payoff amount if you have lived in the house for 11 years(so there are 19

years left on themortgage) and you decide to pay off the mortgage immediately before the 11th

payment isdue?

Suppose you invest $2,000 today and receive $9,500 in five years.

a. What is the internal rate of return(IRR) of thisopportunity?

b. Suppose another investment opportunity also requires $2,000

upfront, but pays an equal amount at the end of each year for the next five years. If this investment has the same IRR as the firstone, what is the amount you will receive eachyear?