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What is the value today of $1,600 per year, at a discount rate of 11 percent,...

What is the value today of $1,600 per year, at a discount rate of 11 percent, if the first payment is received 8 years from now and the last payment is received 30 years from today? Multiple Choice $6,370.55 $6,243.14 $13,326.29 $6,300.66 $2,947.38

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Answer #1

Answer:-

The following informations are given in the question:-

Cash flow per period = $ 1,600

Discount rate = 11% = 0.11

The value of payment 7 years from now is equal to the present value of ordinary annuity (where,  7 years = 8 -1 )

The formula for present value of ordinary annuity is given by:-

Present value of ordinary annuity =   

where, C = Cash flow per period

i = discount rate

n = number of payments  

Present value of ordinary annuity =   

= 1600 x [ (1- 0.0906925) / 0.11]

= 1600 x [ 0.9093075 / 0.11]

= 1600 x 8.26643

= 13,226.291

Present value = 13,226.291 / (1+ 0.11) ^ 7

= $ 6,370.55

Hence, the correct option is A. The value today is $ 6,370.55

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