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6. Terms of two actuarially equivalent annuities: Annuity A: $500 at the end of each of the first 3 months, and $1,000 at the end of each of the next 9 months Annuity B: X at the end of each of the first 2 quarters, and 2X at the end of the next 2 quarters Interest rate: 8% per year, compounded monthly In what range is X?
7. Selected values from a two-decrement table: q1(1)X = 0.03 q(2)X = 0.10 Each decrement is assumed to be uniformly distributed between ages x and x +1 in the associated single-decrement table. In what range is q(r)X ?
8. Smith pays $950 for an investment that returns $500 at the end of year 3, and $700 at the end of year 4. The price is based on a 2-year spot rate of 5.0% and a 4-year spot rate of 7.0%. X = the year 3 forward rate (i.e., the 2-year deferred, 1-year spot rate).In what range is X?
9. Terms of a loan: Amount of loan $75,000 Repayment period 5 years Repayment plans for loan: Repayment Plan #1 Level annual payments at the beginning of each year Repayment Plan #2 Level semi-annual payments at the end of each 6-month period 1000 d(4) = 76.225X = the annual payment under Repayment Plan #1. Y = the total payments in each year under Repayment Plan #2. In what range is X −Y ?
10. Terms of a 20-year annuity-certain: All payments are made on 1/1 Initial payment = $300 Each of the next 9 payments is $300 more than the preceding payment Each of the subsequent 10 payments is $200 less than the preceding payment Interest rate: 7% per year, compounded annually for the first 10 years 6% per year, compounded annually thereafter X = the present value of the annuity immediately before the first payment is made. In what range is X?
