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At an annual effective interest rate of i, both of the following annuities have the present value of X at time 0: (i) a

 

At an annual effective interest rate of i, both of the following annuities have the present value of X at time 0: (i) a 20-year annuity-immediate with an annual payment of 55. (ii) a 30-year annuity-immediate with an annual payment of 30 per annum for the first 10 years, 60 per annum for the second 10 years, and 90 per annum for the last 10 years. Calculate X.

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