Overthinking

I’m probably overthinking all of it.
I appreciate you breaking it down.

Weird thing is I’ve worked with these formulas many times. I know I must ‘know’ them – I used to invest. I have old spreadsheets full of amortization tables, simple and compounding interest, stuff for stocks with dividends, etc.

Ok your interest in assisting me is helping; I’ll try something. I’ll think aloud, reasoning it through best I can. I’ll put dashes to separate this next bit I’m writing:
—–
This formula. What’s it doing? Well, what jumps out?

a) Ok, what’s the relationship between n and t?

t is annual. We do interest on an annual basis as a default. Annual percentage rates are the standard we use for time, represented by t in interest related things.

b) So what’s the n for?

Well, n is there because we don’t compound interest only annually. We also do so several times a year sometimes. So, semiannual (twice a year or 2), monthly (12 times a year or 12), quarterly (4), etc.

c) so why’s the n both inside and outside?

Well, they’ll have to cancel each other out because we want to convert things to annual as that’s the standard we use for interest. So the number of times per year is in the denominator, and the number of times per year is also outside of the parenthesis as part of the numerator.

d) Ok, so why do you need n inside? I get what it’s outside now – because you need it inside.

Right. That’s because of the interest rate. It has to be chopped into whatever number of pieces per year. If it’s once a year, we won’t even see it because by convention we don’t show the 1 in multiplication or when it’s in the denominator. But if it’s more than once a year, we need to see it. But it’s always there though.

The r/n)nt or (interest rate/once a year) * once a year * number of years is there just it is when it’s more than once a year.

e) ok great. So why is the 1+ next to that in the parenthesis?

(this is where I need you to really check my reasoning Aubrey Terrill . All of it but esp this part )

Ah yes. That’s the compounding part. You see, this is percentages we’re dealing with. The 1 is really 100%. So this is 100% of the Principal + the previous compounded interest is represented by the 1 and each time it repeats, the additional interest attaches not just to the principal but to all of the interest that came before it during the compounding process.

f) Ok, so that’s the magic? And Principal is the starting amount.

yes

g) and A is the Amount we’re at in total.

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