Question

2. A young person with no initial capital invests k dollars per year at annual rate of return r. Assume that investments are made continuously and that the return is compounded continuously. a) Determine the sum S(t) accumulated at any time t. b) If r = 7.5%, determine k so that $1 million will be available for retirement in 40 years. c) Ifk = $2000/year, determine the return rate r that must be obtained to have $1 million available in 40 years.

Solve using Matlab
Screen cap the codes plss :((

Answer 1

#S(t)=K*e^(r*t)...this the solution of first part..
r=7.5;              #rate
S=1000000;         #net amount
t=40;              #time..
k=S/(e^(0.075*40))     #K=S/(e^(r*t))...rate=7.5/100=0.075..
disp(k)             #this will display k for second part...

K=2000;         #now K is given       
r1=log(S/K)/40 #r=ln(S/K)/t.... where t=40years...
disp(r1*100)        #will display rate...in %
#so from output we can see that ...
# for second part K=$49787....and for third part rate is 15.537%..