On January 1, 2021, you are considering making an investment that will pay three annual payments of $10,000. The first payment is not expected until December 31, 2024. You are eager to earn 3%. What is the present value of the investment on January 1, 2021?

Respuesta :

Answer:

[tex]PV=26,662[/tex]

Explanation:

this question can be solved by applying the concept of present value:

[tex]PV=FV*(1+i)^{-n}[/tex]

where FV is future value, PV is the present value, i is the periodic interest rate and n is the number of periods. the key here is to make a good counting of the different periods of time, for example if the first payment on December 31,2024 is calculated on Januari 1,2021 there will be 3 years for discounting proccess so:

[tex]PV=10,000*(1+0.03)^{-3}+10,000*(1+0.03)^{-4}+10,000*(1+0.03)^{-5}[/tex]

[tex]PV=26,662[/tex]