Alex Rodriguez recently signed a contract with the Texas Rangers that will pay h

Question

Alex Rodriguez recently signed a contract with the Texas Rangers that will pay him approximately 250 million dollars over the next 10 years. In this problem, assume that he will receive his pay annually in 25 million dollar installments, and that he has just received the first payment. Suppose that he decides to set aside a fixed amount each year to fund a perpetuity of 19500000 dollars per year for his retirement, with the first payment to come in 17 years. If the effective rate of interest is 8.5 percent, how much of his annual salary will be left, after he makes his perpetuity investment?

Explanation / Answer

PV of a perpetuity after 17 years = 19,500,000/0.085 = 229,411,764.7

So this amount after 10 years (17-7)will be 229,411.767.7/1.085^7 = 129,600,751.1

This the FV of the amount to be there after ten years.

So the annual amount taht is to be kept aside for this = pmt(rate,nper,pv,fv,type) Here type = 1 since the investment is made at the beginning of the year

So annual amount =pmt(0.085,10,0,129600751.1,1) =8,051,695.12

So amount of salary left = 25,000,000 - 8,051,695.12 = $16,948,304.88

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