A basketball player received a contract from the New York Knicks in which he was offered 4 million a year for ten years.

Determine the present value of the contract on the date of the first payment if the interest rate is per year, 7% compounded continuously.

Question

A basketball player received a contract from the New York Knicks in which he was offered 4 million a year for ten years.

Determine the present value of the contract on the date of the first payment if the interest rate is  per year, 7% compounded continuously.

anonymous · Answer

"compounded continuously" suggests exponential growth

standard formulas are available for the present value of a string of payments. Usually, they are for yearly compounding, next---

do-it-yourself: PV = 4 + 4/(1.07) + 4(1.07)^2...4(1.07)^9

anonymous · Answer

how did you get that equation?
I just really want to know how to do it so i can understand it myself

loser66 · Answer

I want to clarify the given information: 
Year1 --------------4million
Year2---------------4 million + 7% (4million) ( let say =A)
Year3 --------------A + 7% A 
and so on, right?

anonymous · Answer

ohh okay so you continue to take 7% of the total amount...okay but im not sure what the present value would be..how do u know how many times to take 7%

loser66 · Answer

@douglaswinslowcooper  We need your explanation, please

anonymous · Answer

At the beginning, you got A.

End of that year you got A, also, but the "present value" is the value discounted by the interest you could have gotten if the money had been given to you in the present. 

We "discount" future sums using the interest rate.

If I give you 1000 today and you invest it at 7%, you will have 1000(1.07) at the end of the year., or 1070. If I wait and give you the 1000 at the end of the year, I have deprived you of earning the interest on it, so 1000 in year 1 is worth 1000/(1+.07)=934 today, "resent value. 1000 given to you after two years is worth even less, 1000/(1.07)^2 = 873. 873 today will be worth 873(1.07)^2=1000 two years from now if you invest it at 7% today.

My equation took 4 million immediately and then discounted the next nine payments, by 1/(1.07), 1/(1.07)^2...1/1.07)^9.

Future money is worth less than present money, the difference being greater the larger the interest rate and the longer the time delay in getting your money.

OK?