An investment will pay $50 at the end of each of the next 3 years, $200 at the end of Year 4, $400 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 5% annually, what is its present value? Its future value? Do not round intermediate calculations. Round your answers to the nearest cent.

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TomShelby TomShelby · Answer 1 · 2019-10-11T16:30:21+02:00

Answer:

present value: $ 987.22

future value: $ 1,259.97

Explanation:

We will calculate the present value of each cash flow using the present value of a lump sum:

[tex]\frac{Nominal}{(1 + rate)^{time} } = PV[/tex]

[tex]\frac{50}{(1 + 0.05)^{1} } = PV[/tex]

[tex]\frac{50}{(1 + 0.05)^{2} } = PV[/tex]

[tex]\frac{50}{(1 + 0.05)^{3} } = PV[/tex]

[tex]\frac{200}{(1 + 0.05)^{4} } = PV[/tex]

[tex]\frac{400}{(1 + 0.05)^{5} } = PV[/tex]

[tex]\frac{500}{(1 + 0.05)^{6} } = PV[/tex]

We calcualte and add them all to get the present value

Year Cash flow present value:

1 50 47.61904762

2 50 45.35147392

3 50 43.19187993

4 200 164.540495

5 400 313.4104666

6 500 373.1076983

987.2210613

(we use all decimals as we can't round)

now to get the future value we could do it for each cash flow or bring the present value into the future:

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 987.2210613

time 5.00

rate 0.05000

[tex]987.2210613 \: (1+ 0.05)^{5} = Amount[/tex]

Amount 1,259.97204