TVM calculations (again) Message #1 Posted by Thomas Radtke on 30 Aug 2003, 6:17 a.m.
Hi,
a few weeks ago I complained about some miscalculations concerning TVM and a HP18c et al. The method usually used to calculate the FV for payments that occur at a different period than the interest compoundings is to convert the interest prior to the TVM calculation. Thats not ok if payments are made more often than interest compoundings. I found by iterating over payments and a subsequent iteration over compoundings that
FV=PV*q^j+a*(q^j1)/(q1)
where
a=PMT*(n+p%*(n+1)/2)
if payments are made at the beginning of the payment period and
a=PMT*(n+p%*(n1)/2)
if payments are made at the end of the payment period.
(q=(1+p%),j=interest compounding periods,n=payment periods per comp.period)
Note that the payment convention is strictly german i.e., the PV and PMT are signed (the germans are thinking in 'savings accounts' instead of loans;).
Well, I thought I had something to publish here as noone I asked could tell me anything else than to use the faulty method described first. Too bad, I recently found an older source which mentions equations similar to mine:(. Anyway, I did the same for the case where payments occur less often than interest compoundings and found for begin and end of period payments
FV=PV*q^(n*j)+PMT*q^j*(q^(j*n)1)/(q^j1)
and
FV=PV*q^(n*j)+PMT*q^j*(q^(j*(n1))1)/(q^j1)
(n=payment periods,j=comp.periods per payment period)
respectivly. This isprobably by accident>:)exactly what ICONV+TVM gives (You have to check this by hand as Maple refuses to validate it correctly:). It's just in a more compact shape and easier to use.
bye,
Thomas (Who is still seeking for (i) a job anywhere in the western world and (ii) a cheap 28C to accompany his 18C:)
