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What is the present value today of a deferred annuity of 10 annual payments of $1,000...

What is the present value today of a deferred annuity of 10 annual payments of $1,000 each, if the first payment will be received 6 years from now and the discount rate is 9% EAR? (Round to the nearest whole dollar)

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Answer #1

Given about an annuity,

first payment will be recceived 6 year from now.

annual payment is $1000 for next 10 years

Discount rate d = 9%

So, Present value of annuity 5 years from now can be calculated using PV formula of an ordinary annuity.

PV at year 5 = PMT*(1 - (1+d)^-t))/d = 1000*(1 - 1.09^-10)/0.09 = $6417.66

So, PV today is calculated using PV formula of compunding.

=> Present value today = PV at year 5/(1+d)^t = 6417.66/1.09^5 = $4171.04

So present value today of deferred annuity is $4171.04

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