1. Assume the effective annual interest rate is 11%. Calculate the present value of an annuity of 12 annual payments where the first payment is in 4 years and each payment is $6,000. 2. Assume the effective annual interest rate is 11%. Calculate the future value at the end of the 25th year of $75,000 that is invested at the beginning of the 13th year. 3. Assume the effective annual interest rate is 11%. Calculate the present value of an annuity consisting of 9 annual payments of $28,000 when the first payment is made today. 4. Assume the effective annual interest rate is 11%. Calculate the present value of a perpetuity of annual payments where the first payment is in 18 years and each payment is $45,000. 5. The present value today of an annuity making annual payments of $3,200 starting 8 years from today is $13,465.99. If the fund earns 10.5% /year (effective), how many annual payments (to the nearest whole year) of $3,200 can be made? 6. We expect a cash flow of $80,000 to be received in 85 days. Given a discount rate of 5.75% per year compounded semi-annually, what is the present value of this cash flow? 7. Five months from today your company will begin receiving cash flows of $10,000 paid every 8 months. The last of these $10,000 flows will occur 69 months from today. Calculate the present value (value today) of these cash flows. The discount rate provided to you by your accountant is 5% expressed as a rate per year, compounded quarterly. 8. You have just negotiated a five-year mortgage contract on $200,000, amortized over 25 years with monthly payments, at a rate of 6%. Assume after five years the mortgage rate changes to 5%. What will be your new monthly payments after 5 years? 9. When you retire, you would like to have a monthly pension of $8,000 per month for 30 years. Assume you have just had your 25th birthday and you intend to contribute monthly to your retirement fund until you are 60 . The month after that you will start withdrawing your pension. Your investment advisor has found a guaranteed investment for your fund that will yield 8% per year, compounded quarterly for the duration of your pension needs. How much should you contribute each month to your retirement fund, assuming your contributions start one month after your 25th birthday