What I forgot from Math Class - Compound Interest

Will wonders never cease? Today, more than 14 years after studying math, I finally had to reflect on what I studied. The compound interest formula (CIF from heron in). The reason for this post will be connected to a subsequent post, likely to be named 'Understanding the Backbone of Savings and Loan formulae".

It, as I recall, was my only fond memory from Math. I recall that it 'just made sense'. Well, I forget the actual formula but today I realized it's paramount to review. So, we're gonna do a little Math, kids. This might seem like elementary to you brainiacs at BLIP, but for those under-developed mathletes like myself, read on and get schooled:

Thanks to Wikipedia (which we all know is true and never erroneous) I relearned how important the frequency is in the CIF. I also learned that the frequency must be disclosed to the people involved. That I didn't know.

But let's work the forumula! That's where you can start pluggin' stuff in and having deep feelings of regret over past errors in taking loans, and, if I recall correctly, also where you can realize how much money you WOULD have had....if only you studied harder in Math..

FV = PV(1 + i)n

(I don't know how to make that 'n' superscript, nor how to make that 'i' squiggly and cool like they did at wiki.)

So what does it all mean?

FV = future value (investors drool here)
PV = Present value (investors pull hair out here)
i = fixed interest rate
n = period

By going here you will be able to see variations on the formula like if you want to figure out how much PV you need to get X amount of FV. But that's not FV so who cares?

I decided to do a copy and paste from Wiki because it's cool to see someone else do the work:

Translating different compounding periods

Each time unpaid interest is compounded and added to the principal, the resulting principal is grossed up to equal P(1+i%).

A) You are told the interest rate is 8% per year, compounded quarterly. What is the equivalent effective annual rate?

The 8% is a nominal rate [jargon defined on Wiki elsewhere]. It implies an effective quarterly interest rate of 8%/4 = 2%. Start with $100. At the end of one year it will have accumulated to:
$100 (1+ .02) (1+ .02) (1+ .02) (1+ .02) = $108.24
We know that $100 invested at 8.24% will give you $108.24 at year end. So the equivalent rate is 8.24%. Using a financial calculator or a table is simpler still. Using the Future Value of a currency function, input

• PV = 100
• n = 4
• i = .02
• solve for FV = 108.24

So it does seem that the default for this formula is annual. The example above says 'quarterly' and then you see the /4 cutting the year into 4. So.. I did the math above and it seems to work. That's the one cool thing about Math is that when it works it feels kind of magical. But I'd still rather let someone else do Math and make money and play my guitar.

Let's make a real-life example! Yay!

I bought about $4000 of a failing stock because I didn't know what I was doing. It's value has since dropped to under $2000. So, let's see what I would have had in a simple savings account if I kept it there instead of trying to be a bigshot investor before my knowledge and awareness was at an appropriate level.

PV (back then) = $4000
n= 12 (let's say 12 quarterly cycles have passed even though I didn't buy them all in one shot, close enough for fun)
i = .075% (let's just say that it was an average of 3% compounded quarterly)(and don't forget that little nasty zero because it messed me up. I wrote .75 and I thought I would have been Warren Buffet!)


FV = PV(1 + i)n

FV = 4000(1+.075)(1+.075)(1+.075)(1+.075)(1+.075)(1+.075)(1+.075)(1+.075)(1+.075)(1+.075)(1+.075)(1+.075)

Ok! Drum rollllll!

$9527!

JUMPIN' JEHOSOPHAT BATMAN... I wish I never made this post!

Crap.

Poop.

Let see now

Reality PV (like TV) = $2000
Virtual PV (what i would have had) = $9527
Net loss on this puppy: = -$7527

Well, boys, I think I'm a bit depressed now. I'm quittin' BLIP and putting my money in a high-interest savings account. See you at the top, suckers!