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