Present value of $1 per week at 5% p.a.

I've been desparately trying to work out the underlying formula for the attached table. It is the present value of $1 per week at 5% p.a. If someone could assist me in this, I would be grateful.

It's using a moving average with period 2.

But if you need an equation, you can use the following:

-0.000217*{No. of weeks}^2 + 0.976*{No. of weeks} + 1.84 -1.817

It's a pretty close match to the data, R^2 value is almost 1

Well if the rate is 5% per annum then to find the weekly discount rate you need to take the 52nd root of 1.05 and then subtract 1

1.05^(1/52) -1

This gives a weekly rate of .0938712%

Then you need to work out the annuity factor for the number of weeks.

The formula for this is

1/r[1-1/(1+r)^n]

Where r is the discount rate - i.e. .0938712& and n is the period i.e. the number of weeks.


I suspect they've rounded the discount factor in the sheet, but the above is, to my knowledge, the correct way of doing it.

Hope this helps.