What is the present value of an annuity of $6,000 per year, with the first cash

Question

What is the present value of an annuity of $6,000 per year, with the first cash flow received three years from today and the last one received 25 years from today? Use a discount rate of 7 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

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What is the present value of an annuity of $6,000 per year, with the first cash flow received three years from today and the last one received 25 years from today? Use a discount rate of 7 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

first we shall find the present value of annuity at the end of 2nd year:

present value of annuity = P [ 1 - (1+r)^(-n)] / r

here,

P = $6,000.

r = 7% =>0.07

n = 23 periods........(3 years from today to 25 years from today).

now,

PV at end of second year = $6,000 [ 1 - (1.07)^(-23)]/0.07

=>$6,000 [ 1 - 0.21094688]/0.07

=>$6,000*11.2721871

=>$67,633.12..

now,

value today = A / (1+r)^n

A = $67,633.12

r= 0.07

n = 2

now,

value today

=>$67,633.12 / (1.07)^2

=>$59,073.39.

so the present value of annuity of $6,000 per year received between 3 -25 years from now = $59,073.39

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