Question

Consider 2 annuities that are identical in every way except that one is an Ordinary Annuity and the other is an Annuity Due. Which of these two annuities will have a higher present value assume that the PV in each case is positive?

Answer 1

To explain this assume some numbers;

Amount deposited is PMT =100

No of years N =10

Interest rate per annum R= 10%

Now we will fins the PV of bith cases;

Ordinary annuity

PV=(PMT/R)*(1-(1+R)^-N)

=(100/0.1)*(1-(1+0.1)^-10))=1000*((1-0.385543))

PV of ordinary annuity = 614.46

Now Annuity due:

PV= PV of ordinary annuity * (1+R)

PV= (PMT/R)*(1-(1+R)^-N))*(1+R)

= 614.46*(1+0.1)

PV of annuity due = $675.90

The reason to have high PV for annuity due because we receive the money "Advance" i.e , at t=0 (begin) the money is deposited and for ordinary the money is deposited at the end of month. A 30 or 31 days will have gap which is reducing the PV of ordinary with the effect of discounting.

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