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1. Over a 3-year period, a series of deposits are made to a savings account. All deposits within a given year are equal in size and are made at the beginning of each relevant period. Deposits for each year total $1,200. The following chart shows the frequency of deposits and the interest rate credited for each year: Year Frequency of deposits Interest rate credited during year 1 Semi-annually d (12) = 6.0% 2 Quarterly i (3) = 8.0% 3 Every 2 months δ = 7.0% X = the value of the account at the end of the 3rd year.In what range is X?
2. Terms of two actuarially equivalent annuities: Annuity A Annuity B Issue age 40 40 Type of annuity Perpetuity Life annuity Frequency of payment Monthly MonthlyTiming of payment End of Month End of MonthAmount of each payment P 1,000Selected values: x q x D x Nx 40 0.002125 651 870041 0.002327 607 8049 In what range is P?
3. A participant will retire at age 80.Selected data:p80 = 0.9521 using unprojected mortalityp81 = 0.9461 using unprojected mortalityi = 6.0%, compounded annuallyX = 20 2 a60 using unprojected mortality Y = 20 2 a60 using post-retirement mortality that is projected with 1% annual mortality improvements from this participant’s age 60. Pre-retirement mortality is not projected. In what range is Y/ X ?
4. A portfolio consists of a serial bond with the following terms: Face amount $10,000 Coupon rate 5.0% per year, payable annuallyRedemption At par in two equal installments: the first payable in 9 years; the second payable in 10 years.Yield to maturity 4.0% per year, compounded annuallyX = the modified duration of the portfolio.In what range is X?
5. Retirement benefits for Smith (age 61) and Jones (age 60) payable annually: Smith: a 5-year temporary life annuity-due of XJones: a 10-year certain and life annuity-due of $20,000The present value of Jones’s annuity is 4 times that of the present value of Smith’s annuity.Selected actuarial factors: a60 = 11.53496a 60:10 = 7.26514a62:4 = 3.58056P61 = 0.99394i = 7.0% per year, compounded annuallyIn what range is X?
