Answer:
hi your question lacks the options here is the complete question and options
A local magazine is offering a $2,500 grand prize to one lucky winner. the prize will be paid in four annual payments of $625 each, starting one year after the drawing. how much would this prize be worth to you if you can earn 9 percent on your money
A. $1,848.18 B. $2,024.82 C. $2,545.54 D. $2,450.14 E. $1,934.24
Answer : $2024.82 ( B )
Step-by-step explanation:
The value of the prize if paid in installments
(annual payments) * ( present value of annuity)
first we calculate the present value of annuity
present value of annuity = (1-(1+i)^-n)/i (equation 1)
i = interest earned on prize ( 9% = 0.09 )
n = number of installment payments ( 4 )
present value of annuity = [tex]\frac{ ( 1 - ( 1 + 0.09 )^{-4} }{0.09}[/tex] = [tex]\frac{1- 1.09^{-4} }{0.09}[/tex]
therefore present value of annuity = 3.23972
The value of the prize would be
annual payments ( $625 ) * present value of annuity ( 3.23972 ) = $2024.82
