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 Post subject: What is the best TVM formula to find Time?Posted: Mon, 14 Nov 2011 04:17:13 UTC

Joined: Mon, 17 Oct 2011 20:22:51 UTC
Posts: 5
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?

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 Post subject: Re: What is the best TVM formula to find Time?Posted: Mon, 14 Nov 2011 06:12:16 UTC
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Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3724
Location: Ottawa Ontario
studentmom wrote:
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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