"Bruno Campanini" wrote:
" [...] wrote:
So, these are the exact parameters for your plan [...]:
Loan = 30 180.00
Montly interest = 1.2416768%
Terms = 60 months
[....]
I think you intended to write 1.2416667% (14.9%/12).
I suspect that [...] you rounded that to 15.961%,
you tried to reverse-engineer the monthly rate with:
(1 + 0.15961)^(1/12) - 1 = 1.2416768%.
[....]

No. I calculated effective montlhy rate of interest
from:
1 - principal 30 180.00
2 - terms = 60 month
3 - montly payment = 716.40

Then I compute 1.24168311% = RATE(60,716.40,-30180).
If you continue to disagree, please provide the
exact formula or method and numbers that you use
to compute 1.2416768%. I would be very interested
-- no pun intended ;-).

This is the only mathematically-correct way to
make such calculations.

No need to pontificate. You are preaching to the
choir. I was not questioning your methods, merely
your number.

If by "mathematically correct", you mean a monthly
interest rate that reduces the principal to zero
with 60 payments all of which are $716.40, then
RATE(60,716.40,-30180) -- approx 1.24168311% --
is the correct rate, not 1.2416768%. This is
self-evident if you build an amortization table
and dispense with any rounding. With 1.2416768%,
the last payment must be $716.29, whereas with
RATE(60,716.40,-30180), the last payment is
"exactly" $716.40, formatted to 6 decimal places.

Alternatively, you can use the following formula:

FV = (-30180 + 716.40*(1 - (1+i)^(-60))/i)/((1+i)^(-60))

When i = 1.24168311%, FV is nearly zero (-7E-6);
FV is -2E-8 when i = RATE(60,716.40,-30180).
When i = 1.2416768%, FV is 0.11, indicating that
that 60 payments of $716.40 is too much. $0.11
is consistent with requiring the last payment to
be $716.29 ($716.40 - $.11) in the aforementioned
amoritzation table.

No matter! I think you make the important point
that lenders might use (1 + 14.9%/12)^(12/365),
not 14.9%/365, to determine the effective daily
rate. The first formula yields the same effective
annual rate as the nominal monthly rate (14.9%/12).
Arguably, that does seem more "mathematically
consistent".

I cannot say for sure at this time which formula
lenders use -- or even if they all make the same
choice.