# Differences between present value and future value?

I have a difficult time understanding the definitions ofpresent value and future value

I

I think when calculating future value, you'll calculate what you'll receive in the future.

and i get confused about the present value definition

please explain fully for me. thank you

Relevance

Present value is the value today of a stream of payments to be received in the future at a given cost of capital. Future value is the value of a stream of payments at some point in the future.

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• Good question, I had trouble with this when I first started taking classes at MIT. I will list the equations for each then explain them to the best of my ability.

PV = FV/(1+r)^t

FV = PV(1+r)^t

Now for future value, you take the amount of money you have now, and multiply it by 1 + r which is the interest rate or the rate of return the bank or the investment is going to add back to your money. say 10%? r is a decimal since it is a percentage, and so 1 + r = 1 + 0.10 if the rate of return was 10%.

Next you figure out if the rate of return is the annual compounding rate or if it is monthly or whatever. Lets say 10% is the yearly compounding interest rate. This means that at the end of the first year, your money will = 1.10(present value). and at the end of the second year it will be worth 1.10(1.10(present value or starting value)

1.10(1.10(PV) also = PV(1.10^2) where 2 is the amount of years that have passed on your investment.

t = the time that passes/the compounding interval

so t = 2 years/1 year since 2 years have passed and the compounding interval is 1 year (you get 10% every year)

Thus, FV = PV(1 + r)^t

Sometimes you will be given the future value, and you might like to know how much that value will be worth TODAY. So if your friend tells you that he will pay you \$100 in 2 years for the radio you sold to him, you should know that \$100 in 2 years is worth less today if the interest rate rises.

PV of \$100 in 2 years :

PV = FV/(1 + r)^t

PV= 100/(1+interest rate)^2

100/(1.04^2) = \$92.46

If the radio is worth \$100 today, you would want him to pay you :

FV = 100(1.04)^2 = \$108.16 in 2 years

HOPE THAT HELPS!

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• present value is what it is worth NOW.

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