The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

firemeboy · Daedalian Member

I remember in algebra we learned a formula that allowed you to figure the interest you would earn if you saved a given amount of money. Does anybody know this formula, or how to figure your interest? I am not just talking 10 percent of 1000 dollars. This is where the interest is compounded daily or constantly. Anybody? Anybody?

Ghost Post · Icarian Member

I believe the formula is:

A(n) = P*((I+1)^n)

where A(n) is the amount of money at time n and n is in units of how often interest is compounded. In other words if the interest is compounded monthly n is the number of months, if annually n is the number of years. P is the principle amount invested. A(0) = P. I is the interest rate per time period (10% -> I = .10). If you have an annual interest rate of 12% but it is compounded monthly you should use I=.01, not .12 (I'm not possitive if this is actually how banks, etc do this.)

Here's how I came up with the formula:

the amount at time n is the amount from the previous month plus the interest earned on that amount:
A(n) = A(n-1) + A(n-1)*I = A(n-1) * (1+I)

Similarly A(n-1) = A(n-2) * (1+I)
and so A(n) = A(n-2) * (1+I)^2
Following this reasoning I get that A(n) = A(0) * (1+I)^n

I haven't worked out the formula for when the interest is compounded continuously yet. That is a bit trickier.

[This message has been edited by Drew (edited 02-24-2000).]

Quailman · His Postmajesty

One minor point that needs to be spelled out - the Interest rate (I) must be stated in the same time period as the compounding cycle. In other words, if the rate is 12% and the interest is compounded monthly, then the monthly rate would be 1%. If compounded quarterly, use 3% (12%/4).

firemeboy · Daedalian Member

Thanks Quail. I remember that there was a way to do it continuously, and the funny part was that it didn't make a whole lot of differenct. Apparently a few decades ago the banks came out with this concept and people moved their money around trying to get the best deal. It was all so close there wasn't much of a difference. Or so Mr. Johnson said.

Ghost Post · Icarian Member

Ok, I think I have the continuous formula:

A(n) = P * e^(I*n)

Where I is the interest earned over a given time period and n is the number of those periods. I got this formula in pretty much the same way as the previous one, taking the limit as the time between interest payments went to zero.

mathgrant · A very tilted cell member

Bump.

------------------
"Mathematics is like the Nile, begins in minuteness, ends in magnificence." --Charles Caleb Colton