1.Find the present value of an annuity which pays continuously at a rate of $1000 per year for 8 years, given that the effective annual interest rate is 5%.

2.Given t = (1 +t) 1 , find the accumulated value (at the end of six years) of an annuity which pays continuously at a rate of $500 per year for six years.

3.There is $40,000 in a fund which is accumulating at 4% per year convertible continuously. If money is withdrawn continuously at the rate of $2400 per year, how long will the fund last (to the nearest tenth of a year)?

4.Annuity #1 pays $10,000 per year continuously for one year. Annuity #2 has one payment of $10,000 (it is strange to call it an annuity, since it has only one payment). The annual effective interest rate is 5.5%. At what time should Annuity #2 have the payment, so that the two annuities have the same present value at time 0?