How the hell did I do the math wrong?
- snip -
Not a diss, Danny, but please follow-up if again I'm truly in error, bud.
You are correct that it needs to increase by a flat amount of $2.994 per day, and if you had said that I wouldn't have corrected you.
You are also correct that it needs to increase by a flat amount of $8.982 every 3 days, and if you had said that I wouldn't have corrected you.
However, what you said was that it needed "a 1% rise on average every three days", and that's where you made the mistake.
Certainly, $8.982 is approximately 1% (pretty close to 0.92%) of the CURRENT $976, but it is less than half a percent of $1952 which you'll be calculating 1% of about a week before we reach $2000.
If the exchange rate rose by 1% (
$9.76) in the next 3 days then the new rate would be $985.76.
A 1% increase on that over the next 3 days would be an increase of
$9.8576 (bringing the new rate 6 days from now to $995.6176).
Another 1% increase on that over the next 3 days would be an increase of nearly
$9.9562 (bringing the new rate 9 days from now to more then $1000).
Now (9 days from now) 1% is no longer $9.76, it's
more than $10.
That increase keeps getting bigger and bigger since the amount that you are taking 1% of is getting bigger. By the end of 335 days, the rate has grown to nearly $3000.
With a 1% increase every 3 days you'd get to $2000 in about 217 days. After that, your 1% increase will be more than $20 every 3 days.
If you just go with a flat amount of $8.982 every 3 days, then the percent increase gets smaller as the exchange rate increases (since the numerator of your division isn't changing, but the denominator is growing).