Where the constant comes from in the Compound Interest formula?

Question

I want to understand where the 1 constant comes from in the Compound Interest formula.

I'm a programmer, I can find a logical way to calculate it using a programming language, this is a way I can actually understand:

P = 6000
t = 12
interestRate = 1.11

for i in range(0, t):
    interest = P * interestRate / 100;
    P += interest

print P

I would never use this in production environment, but it's the way I can understand. However looking at the following formula:

$P(1 + r)^t = F$

For instance, I can relate the ()^t to a for loop. But the constant get's me wondering.

Can anybody explain why there is the constant number one (1) in the formula?

It may sound silly, but I'd like to know the thought process to get to this formula if it's not asking too much. If you can relate to programming, even better for me.

Thanks!

Answer 1

If the power is the loop, then the $1+$ hides in the += assignment. Expand it to

P = P + interest

or further to

P = P + P * interestRate / 100

and finally simplify to

P = P * (1 + interestRate / 100)

and you are there.

Answer 2

The reason for the constant $1$ in the parenthesis is that the rate $r$ is typically written as a percentage less than $100.$ We need to add by $1$ so that we are multiplying each time by a factor more than $1.$ Our money should increase, not decrease.