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Future values of the ordinary annuities

Question 1: Find the future values of the following ordinary annuities:

a. FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded semiannually?

b. Fine of $200 each 3 months for 5 years at a nominal rate of 12%, compounded quarterly?

c. The annuties described in parts a and b have the same amount of money paid into them during the 5-year period and both earn interest at the same nominal rate, tye annunity in bart b earns $101.75 more that the one in part a over the 5 years. why does this occur?

Question 2: Assume that your father is not 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is until he is 85. He wants his first retirement payment to have the same purchasing power at the time he retires as $40,000 has today. He wants all his subsequent retirement payments to be equal to his first retirement payment (do not let the retirements grow with inflation: he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will began the day he retires, 10 years from today, and he will than get 24 additional annual payments. Inflation is expected to be 5% per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his savings of 8% per year, annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year) to meet his retirement goals? (Hint: neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.

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