Question

determine the present vlaue of $1,200 per year, at a discount rate of 10%. If the first payment is received 5 years from now and the last payment is received 22 years from now?

Answer 1

Given that first payment is received at 5 years from now and last payment is received at 22 years from now.

So, Present value wil be 1200/(1.1)^5+1200/(1.1)^6+.....1200/(1.1)^22.

We can consider this payments as Annuity for 22 Years-Annuity for 4 years. It means,

(1200/1.1+1200/1.1^2+....1200/1.1^22)-(1200/1.1+1200/1.1^2+..1200/1.1^4).

We know that present value of annuity formula is (P*(1-(1+r)^-n))/r. So,

(1200*(1-(1.1)^-22)/0.1)-(1200*(1-(1.1)^-4)/0.1= 10525.85-3803.839= 6722.01

So, present value of the payments is $6722.01