Question

You are scheduled to receive annual payments of $21,400 for each of the next 23 years. Your discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

Answer 1

We know that, there are two types of annuities, Ordinary Annuity and Annuity Due. Annuity ordinary is when the payments are made at the end of each yera and Annuity Due is when the payments are made at the beginning of each year.

Given that,

A = $21,400

n(no. of years) = 23

i(discount rate) = 8% = 0.08

PVA(ordinary) = A*(1/i - 1/(i(1+i)^n)

substituting above values gives us

PVA (ordinary) = $221,940

PVA (due) = [A*(1/i - 1/(i(1+i)^n)] *(1+i)

substituting above values gives us

PVA (due) = $239,695

Annuity due will have greater cash flow because payments are received one year sooner.

The difference is thus of $17,755