Suppose that a sum S0 is invested at an annual rate of return r compounded continuously. a. Find the time T required for the original sum to double in value as a function of r. b. Determine T if r = 7%. c. Find the return rate that must be achieved if the initial investment is to double in 8 years.

Answer

given,

Sum = S₀

annual rate of return = r

T is the time

Ordinary differential equations is

integrating both side

e^C = S₀

a) time when sum is doubled

b) Time T if r = 7 %

        T = 9.9 years.

c) return rate, r = ? T = 8 years

         r = 0.0866

        r = 8.67%

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2