MHB Calculating Loan Payments: A Simple Formula

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The discussion focuses on calculating loan payments using a formula based on the initial loan amount, future balance, monthly payment, number of payments, and interest rate. An example is provided with specific values illustrating how monthly payments reduce the balance over time. The user seeks a formula to express the monthly payment in relation to these variables. The conversation highlights the importance of understanding loan payment calculations for financial planning. The user also shares their own formula to ensure it is recorded.
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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:
Code:
   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
 
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My formula (in case I lose it!)
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!
 
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