Question

9. Find the geometric return for a portfolio of stocks that return 12%, 3%, negative -2%, and 8%

9A. Calculate the Future value of an annuity due where you invest 2,000.00 per year for 25 years if you have a 9 % return? If the return is lowered, what happens to the PRESENT Value of the annuity due?

Answer 1

Q9:

Geometric return =[(1+r1)(1+r2) ... (1+rn)]^(1/n) -1

=[(1.12*1.03*.98*1.08)]^(1/4) -1 =5.117%

Q9A:

FV of annuity due is given below

where C= annuity payments ; i=interest rate ; n= no of terms

FV= [2000*[(1.09)^25 -1]/.09]*1.09 =184647.95

PV of annuity due is given below

PV= [2000*[1-(1.09)^-25]/.09]*1.09 =21413.22

lets lower interest rate to 7%

PV=[2000*[1-(1.07)^-25]/.07]*1.07= 24938.6 --- PV increases