Problem 1:(18 points; 3 points each)

Answer the questions below.Each question is self-contained and independent from the others.

a.The stated annual interest rate is 2 percent, couponed continuously.What is the equivalent effective annual interest rate (to 6 places past the decimal point) associated with this stated rate?

b.The effective monthly rate is .0025 (i.e., a quarter of a percent per month).If you have a 30-year mortgage for $500,000 with monthly payments, what are your monthly payments?

c.What is the present value (i.e., the value at t = 0, where t counts years) of the following stream of payments if the effective annual interest rate is .03 (i.e., 3% per annum):The first payment of $100 is made in 10 years (at t = 10).There are 10 more payments after that first payment that occur every 1.5 years.Each of these subsequent payments are 5% larger than the previous payment.

d.You need to borrow $20,000 to buy a car.Bank A is charging you a stated rate of 4% compounded every month; you must make monthly payments for 5 years.Bank B is charging you 3.9% compounded continuously; you also must make monthly payments for 5 years.Which deal do you like better: Bank A's or Bank B's?

e.You need to borrow $20,000 to buy a car.Bank X is charging you a stated rate of 6% compounded every month; you must make monthly payments for 5 years.Bank Z is charging you 5.9% compounded continuously; you also must make monthly payments for 5 years. Which deal do you like better: Bank X's or Bank Z's?

f.What is the present value of an annual payment stream that starts next year at $100 and grows 3% every year thereafter into the infinite future is the discount rate is an effective 5% per year?