ACTUARIAL: INTRODUCTION TO FINANCE OF MATHS

6. An annuity is payable in arrears for 15 years. The annuity is payable half- yearly for the first 5 years, quarterly for the next 5 years, and monthly for the final 5 years. The annual amount of the annuity is doubled after each 5-year period. On the basis of an interest rate of 8% per annum convertible quarterly for the first 4 years, 8% per annum convertible half- yearly for the next 8 years, and 8% per annum effective for the final 3 years, the present value of the annuity is 2,049. Find the initial annual amount of the annuity.

Answer: $199.99 (Note that at 4%, i^(6) = 0.039349