find the amount of a continuous money flow in three years if the rate is given by f(t)=1000-t^2 and if interest is 5% compounded continuously
To find the amount of a continuous money flow in three years with a rate given by f(t) = 1000 - t^2 and interest of 5% compounded continuously, we can use the formula for continuous compounding:
A = P * e^(rt)
where:
A = amount of money after t years
P = initial amount of money
r = interest rate (as a decimal)
t = time in years
Since the rate is given by f(t) = 1000 - t^2, we can calculate the interest rate at t = 3 years:
r = f(3) = 1000 - 3^2 = 1000 - 9 = 991
Now, we can plug in the values into the continuous compunding formula:
A = P * e^(0.05 * 3) = P * e^(0.15)
So, the amount of money after three years would be P * e^(0.15).