Question: A geometric annuity, an arithmetic annuity, a level pay annuity and a level pay perpetuity all have the same present value. All 4 annuities pay

A geometric annuity, an arithmetic annuity, a level pay annuity and a level pay perpetuity all have the same present value. All 4 annuities pay monthly and are annuities immediate. The interest rate is 4.35% compounded semi-annually. The first 3 (not counting the perpetuity), all end in 7 years. The perpetuity has level payments of $550. The geometric annuity has a growth rate of 0.65% per period. The arithmetic annuity's first payment is $Q and each subsequent payment increases by $Q. a) What is the value of the perpetuity? b) What is the amount of the payment for the level pay annuity? c) What is the initial payment for the geometric annuity? d) What is $Q for the arithmetic annuity? e) If the interest rate changes to 5.85% (same compounding), which annuity makes the most (or loses the least) amount of money based on the new interest rate?

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