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Solving the TVM equation for the interest rate
02-12-2020, 12:31 PM (This post was last modified: 02-12-2020 05:51 PM by Albert Chan.)
Post: #17
RE: Solving the TVM equation for the interest rate
(02-12-2020 10:50 AM)Gamo Wrote:  Suggested Guess Formula:

[((FV/PMT) - n) x 2] ÷ [(n - 1)^2 + (FV/PMT)]

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Example:

$40,000 to be accumulated in 11 years; annual payments of $2,564

The interest rate needed is approximately _____ %.

Using the Suggested Guest routine i = 0.0796

Answer: Interest Rate = 0.0678 or 6.78%

I found that harmonic mean of two extreme guesses gives good rate estimate (M=PMT, F=FV, P=PV)

I1=(F+P+M*N) / (N*((1-N)/2*M - P))
I2=(F+P+M*N) / ((N-1)/2*(F-P) - P)

I1 assumed no compounding, thus over-estimate the rate, by quite a bit.
I2 over-estimated compounding effect, thus under-estimated rates, is better estimate than I1.
For how it is derived, see https://www.hpmuseum.org/forum/thread-14...#pid125408

For above example, N=11, F=40000, P=0, M=-2564

I1 = 11796/141020 ≈ 8.365%
I2 = 11796/200000 ≈ 5.898%

I ≈ 2/(1/I1 + 1/I2) = 11796/((141020+200000)/2) = 11796/170510 ≈ 6.918%, over-estimated 0.138%

Or, we can skip I1,I2: I ≈ 4*(F+P+M*N)/((N-1)*(F-M*N)-(3*N+1)*P)
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RE: Solving the TVM equation for the interest rate - Albert Chan - 02-12-2020 12:31 PM



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