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

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