Graham receives $640,000 at his retirement. He invests X in a twenty year annuit

Question

Graham receives $640,000 at his retirement. He invests X in a twenty year annuity-immediate with annual payments and the remaining $640,000 - X is used to purchase a perpetuity-immediate with annual payments. His total annual payments received during the first twenty years are twice as large as those received thereafter. The annual effective interest rate is 5%.

Find X

Explanation / Answer

im pretty sure its 0.05X/(1-(1.05^-20)) >>> gives 0.0802425X >>> which is the annual payment then 640,000 - X = (1/0.05)(0.0802425X) 640000 = 2.60485X X ~ $245,695 does this sound correct?

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