S.O.S. Mathematics CyberBoard

I have the payment amount, principal value, and interest rate but the question asks for the time. Of course I used my TI83 TVM solver and got the answer but if you were doing it with pencil and paper what formula would you use?

Ok, Mom; this is the formula to calculate the monthly payment:
P = Ai / [1 - 1/(1 + i)^n]
P = monthly Payment
A = Amount borrowed
n = number of months
i = interest rate MONTHLY; like, if 9% annual, then .09/12 = .0075

You want this in terms of n, so we need to isolate the n:
P = Ai / [1 - 1/(1 + i)^n]

P[1 - 1/(1 + i)^n] = Ai

P - P/(1 + i)^n = Ai

P/(1 + i)^n = P - Ai

(1 + i)^n = P / (P - Ai)

n = LOG[P / (P - Ai)] / LOG(1 + i)

Amen

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