This is actuarial science.

Problem 1 - Unknown and Varying Interest The PV of an annuity-immediate with quarterly payments of $450 for 6 years is $9457.59 . a) Determine the nominal annual rate of interest compounded quarterly. i(4)= % b) Determine the effective annual rate of interest. i= %

Problem 2 - Unknown and Varying Interest The PV of an annuity-due with annual payments of $555 for 16 years is $6520.78 . Determine the effective annual rate of interest. i= %

3.

Annual deposits of $80 are made at the beginning of each year for 15 years. Find the PV of this annuity-due if the effective annual rate of interest is 3% for the first 6 years and 5% for the last 9 years. PV =

4.

Annual deposits of $400 are made at the end of each year for 15 years. The first 4 deposits are invested in a fund that pays an effective annual rate of interest of 8% The remaining deposits are invested in another fund that pays 6% effective. Find the AV of these deposits at the end of 15 years. AV =

5.

Annual deposits of $20 are made at the beginning of each year for 18 years. Find the AV of this annuity at the end of 18 years if the effective annual rate of interest is 6% for the first 5 years and 8% for the last 13 years. AV =