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A financial security offers the security holders multiple payments as follows: $50 semi-annually for 10 years,...

A financial security offers the security holders multiple payments as follows: $50 semi-annually for 10 years, with the first $50 to be paid a half year from now, and an additional single payment of $1,000 ten years from now. Assume the appropriate APR for this security is 8%, how much should this security sell today?

Select one:

a. $1135.90

b. $1188.26

c. $972.5

d. $1008.75

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Answer #1

Rate = 8% / 2 = 4%

Number of periods = 10 * 2 = 20

Present value of annuity = Payments * [1 - 1 / (1+ r)^n] / r

Present value of annuity = 50 * [1 - 1 / (1+ 0.04)^20] / 0.04

Present value of annuity = 50 * [1 - 0.456387] / 0.04

Present value of annuity = 50 * 13.590326

Present value of annuity = $679.516317

Present value of future cash flow = Futuer value / (1 + r)^n

Present value of future cash flow = 1000 / (1 + 0.04)^20

Present value of future cash flow = 1000 / 2.191123

Present value of future cash flow = 456.386946

Price = 679.516317 + 456.386946

Price = $1,135.90

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