MHB Calculating Loan Payments: A Simple Formula

[Wilmer]

I thought this was "INTERESTing".
You want to borrow a dollars, with monthly payment of p dollars, such
that you'll owe f dollars after making n payments, at monthly rate r%.
Example:

   MONTH    PAYMENT        INTEREST   BALANCE
     0                                3000.00
     1      -522.56         30.00     2507.44
     2      -522.56         25.07     2009.95
     3      -522.56         20.10     1507.49
     4      -522.56         15.07     1000.00

So, in example: a=3000, f=1000, p=522.56, n=4, r=.01

Devise a formula calculating p in terms of a, f, n, r

 

[Wilmer]

No takers?

My formula (in case I lose it!)

Spoiler

a = amount of loan
f = future amount of loan
n = number of monthly payments
r = monthly rate
p = payment amount

p = r[a * (1 + r)^n - f] / [(1 + r)^n - 1]

...anutter useless formula!