Present Value of an Annuity - Understanding

Hi all,

The question is:
A beneficiary will receive AUD 1,000 per year cash flows for 10 years from an ordinary annuity. The first cash flow is expected at the end of Year 8, and the discount rate is 10%. Today’s worth of this annuity is closest to? Answer is: 3,153

Ok, so the calculation goes:

  1. PV of 10years of annuities of 1,000 at 10% is for calculator: N=10, i/y = 10%, 1000 = PMT, 0=FV, and PV is = 6,144.57

  2. (here is problem), the second PV calculation: FV is = 6,114.57, i/y = 10%, PMT = 0, and N needs to be =7, to arrive at correct answer of PV = 3,153

When I did this for the first time in the 2) part of the calculation I instinctively put N=8. If the CF is at the end of Y8, I assume there are 8 years for discounting. I’m having a bit of trouble to understand this, why I need to use N=7 if it is at the end of year 8?

And, if the original question was “at the beginning of year 8”, would I then need to use N=6 in the second part of my calculation?

Thank you in advance, I would like to understand this better and not just memorize what I need to use in calculation!

Everything hinges on whether you have your calculator in END mode or BGN mode.

In END mode with the first payment at the end of year 8, the PV will be as of the beginning of year 8; i.e., the end of year 7.

In BGN mode with the first payment at the end of year 8 (i.e., the beginning of year 9), the PV will be as of the beginning of year 9; i.e., the end of year 8.

If you draw a time line for these questions, you’ll find that they’re much clearer and you’ll make far fewer mistakes.

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Definitely draw the timelines as is often suggested. While a financial calculator is helpful, I strongly recommend that you learn to solve these problems without relying on them.

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Indeed it is more clear when put on paper and drawing timeline really helps. I tried to do it in Excel and got it.

Thank you both!