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3. You are given a perpetuity with annual payments as follows... - Payments of 1 at the end of the 1st year and every 3 years thereafter - Payments of 2 at the end of the 2nd year and every 3 years thereafter - Payments of 3 at the end of the 3rd year and every 3 years thereafter The interest rate is 4% convertible semiannually. Calculate its present value 4. You are given a 20-year annuity immediate paying 10 for 10 years, then the amount decreases by 1% per year for 10 years. The annual effective interest rate is 3.5%. Calculate the present value of this annuity. 5. Find the present value of a perpetuity that pays $10 one year from now and each subsequent yearly payment is 2% more than the previous one. Find the present value if the interest rate is 4% compounded annually. 6. An annuity makes continuous payments of $100 per year for 6 years beginning today. The force of interest is given by t={0.30.4/t0t3t>3. Find the future value six years from now