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Re: Re: Re: Math help

When I plug the values into an Excel worksheet, yours and John's answer is correct. Reversing the order seems to add a year.

This is a trick question, since the value of 265 is never obtained. At 83 years, the value is slightly above 265, and at 84 years the value is slightly below 265. We're compounding at one-year intervals.

Jim

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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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: Math help

Not quite. The change is by a factor of log(1.015)/log(1.005), which is 2.985.

Re: Re: Math help

Thank you very much.
I hope you stay well.