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Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today

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facundobuzzetti

Answer:

The annuity will cost him $963,212.95.-

Explanation:

Giving the following information:

Cash flow= $75,000

Interest rate= 0.0525

n= 20

First, we need to calculate the final value. We will use the following formula:

FV= {A*[(1+i)^n-1]}/i + {[A*(1+i)^n]-A}

A= annual cash flow

FV= {75,000*[(1.0525^20) - 1]/0.0525} + {[75,000*(1.0525^20)] - 75,000}

FV= 2,546,491.88 + 133,690.82= $2,680,182.70

Now, the present value:

PV= FV/(1+i)^n

PV= 2,680,182.70/(1.0525^20)

PV= $963,212.95

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