Question

3) Find the present value of a 20 year annuity due where payments are $1,000 at the beginning of the first year, third year, etc. and payments are $1,500 at the beginning of the second year, fourth year, etc. Here effective annual interest is 5% Hint: Draw a time diagram!!!

Answer 1

Annuity can be broken down into two annuities-first annuity starting at the beginning of the first year and second annuity starting at the beginning of the second year

Present value of first annuity=1000+1000/1.05^2+1000/1.05^4....=1000*(1-1/(1.05^2)^10)/(1-1/1.05^2)=6702.238

Present value of second annuity=1500/1.05^1+1500/1.05^3+1500/1.05^5...=1500/1.05*(1-1/(1.05^2)^10)/(1-1/1.05^2)=9574.625

Present value of annuity=6702.238+9574.625=16276.863