A machine is purchased by making payments of $5000 at the beginning of each of the next five years The interest rate was 10%. The future value of an ordinary annuity of 1 for five periods is 6.10510. The present value of an ordinary annuity of 1 for five periods is 3.79079. What was the most of the machine?

5000 x 3.79079 =18954

Is this correct?

Well, it is a present value since you're looking for today's price, but the fact that the payments are at the beginning of each year instead of the end of each year makes it an annuity due, not an ordinary annuity. Do you have charts for annuity due?

I do have the charts, but I am supposed to use the numbers in the problem.

Okay, if you're limited to using the given info, then you're halfway home. Your computation, using the "ordinary" annuity factor, has given you the present value of the cash flows one year prior to the first cash flow; i.e. one year prior to the date the machine was purchased.

So to get the machine's effective cost on the date of purchase, you need to "future value" your answer forward by one period. You'll do that by multiplying your answer by 1.1. (Can you seen why, given that the interest rate is 10%?)

That'll give you the same answer you'd have obtained directly from a "PV of an annuity due" factor.

That's a whole lot easier than the adjustment I learned. I'll definitely have to remember that!

Yep, the fact that "this year's annuity due is just last year's ordinary annuity" comes in kind of handy on occasion, for a fast conversion from one to the other.

In fact, if you lay an ordinary annuity PV (or FV) table and an annuity due PV (or FV) table side by side, you'll see that every number on the AD table is just its counterpart number from the OA table, multiplied by (1 + r), with r being the discount rate for the number you're looking at.

Like, say, the PV of an OA, at 4%, 9 payments, is 7.43533. For the same 4%, 9 payments, the PV factor from the AD table is 7.73274, which is just 7.43533(1.04).