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Peter Lynchpin wants to sell you an investment contract that pays equal $13,400 amounts at the end of each year for the next 24 years. If you require an effective annual return of 7 percent on this investment, how much will you pay for the contract today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value today

Respuesta :

ajeigbeibraheem

Answer:

P = $153689.08

Step-by-step explanation:

Present value annuity is used as today's price to solve this question and its formula is given as:

[tex]P = C (\frac{1-(\frac{1}{1+r})^n}{r})[/tex]

where;

C = Yearly Payment= $13,400

r =rate of interest = 7% or 0.07

n= no of years=24

[tex]P =13,400 (\frac {1-(\frac{1}{1+0.07} )^{24}}{0.07})[/tex]

[tex]P =13,400 (\frac {1-(\frac{1}{1.07} )^{24}}{0.07})[/tex]

[tex]P = 13,400(\frac {1-(\frac{1}{5.072366953} )}{0.07})[/tex]

[tex]P = 13,400(\frac {1-0.19714662}{0.07})[/tex]

[tex]P= 13400(\frac{0.80285338}{0.07})[/tex]

[tex]P = 13400*11.469334[/tex]

P = $153689.0756

P = $153689.08   (to 2 decimal places)

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