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
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?
3 answers
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
how did u get 10000