### Number Watch Web Forum

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Re: Re: Re: Re: Math help

In 7th grade, they taught us the sales discount equation. I learned then that 40% off is not the same as 40% more than the discounted price. You are usually in the same ballpark, but you might be short of the wall by a few meters (or maybe many) meters.

Re: Re: Re: Math help

My mistake is falling for the continuity trap. If we put the non-swapped values into the continuous formula, we get the same answer as before:

265 = 937*e^(-0.015*t)
ln(265) = ln(937) -0.015*t
t = (ln(265 – ln(937))/(-0.015) = 84.1969 years

However, putting the correct values into the correct formula give us a slightly different answer. If we set A = 265, P = 937, r = -1.5%, and n = 1; we get:

265 = 937*(1 -0.015/1)^(1*t)
ln(265) = ln(937) +t*ln(0.985)
t = (ln(265) – ln(937))/ln(0.985) = 83.5638 years.

But we can’t get 265 exactly. We are slightly above it at 83 years and slightly below it at 84 years.

Jim

you can also use a spreadsheet

If you don't know math, you can also calculate it using excel:
type 937 in box A1
type =A1-0.015*A1 in box A2
drag down
in box A85 you'll see the number 263.2588
So after 84 years.

Re: you can also use a spreadsheet

If the rate of reduction was .5% instead of 1.5%, would the number of years be increased 3 fold to about 255 years?

Re: Re: you can also use a spreadsheet

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