Asked by C
A wealthy patron of a small private college wishes to endow a chair in mathematics with a gift of G thousand dollars. Suppose the mathematician who occupies the chair is to receive $110 thousand dollars per year in salary and benefits. If money costs 8% per year compounded continuously, what is the smallest possible value for G?
Answers
Answered by
Reiny
So they will need as much in the account to annually generate 10,000 in interest
x e^.08 - x = 10000
x(e^.08 - 1) = 10000
x = 10000/(e^.08 - 1) = $120,066.66
Since G is supposed to in thousands
G ≥ 120.06666
check:
amount of the 120066.66 after 1 year of continuous growth of 8%
= 120066.66 e^.08 = 130066.66
amount earned for math guy = 130066.66-120066.6
= 10,000
x e^.08 - x = 10000
x(e^.08 - 1) = 10000
x = 10000/(e^.08 - 1) = $120,066.66
Since G is supposed to in thousands
G ≥ 120.06666
check:
amount of the 120066.66 after 1 year of continuous growth of 8%
= 120066.66 e^.08 = 130066.66
amount earned for math guy = 130066.66-120066.6
= 10,000
Answered by
Bill
Since it's compunded continuously, you use Present Value =
Integrate from 0-T f(t)e^(-rt).
It doesn't give a time limit, so we'll assume it's infinte.
Integrate from 0-Infinity 110e^(-.08t)
=[-1375e^-.08(Inifinity)]-[-135e^-.08(0)]
= 0-(-1375)
= 1375
Integrate from 0-T f(t)e^(-rt).
It doesn't give a time limit, so we'll assume it's infinte.
Integrate from 0-Infinity 110e^(-.08t)
=[-1375e^-.08(Inifinity)]-[-135e^-.08(0)]
= 0-(-1375)
= 1375
Answered by
Hamna
how did u get 10000
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