Question

If the present value of an ordinary, 2-year annuity is $6,600 and interest rates are 10 percent, what's the present value of the same annuity due?

Answer 1

In order to calculate the value of the same annuity as if it were annuity due, we could easily use the mathematical approach, where we first find the value of annual payments given the PV of ordinary annuity and then use that to calculate the PV of annuity due. But this is a longer approach.

Before I explain the short cut for the question, let me show the mathematical relations for PV of ordinary annnuity and annuity due:

where R are the annual payments, i s the interest rate and n is number ofperiods. Now look at these relations carefully, You should be able to deduce from the two relations that:

PV of Ordinary Annuity * (1 + i) = PV of Annuity Due

We will use the same relation:

PV of Annuity Due = 6,600 * (1 + 10%) = $7,260