The calculation was explained to me as 6% per annum.......I assumed from
that it was compounded each year....as you have explained.......I will need
to double check I have the correct understanding of the required calculation.
The seed of doubt!
A pretty big seed, IMHO. To some degree, it depends on the type of
financial institution. A mutual fund or other securities investment
is likely to mean APY -- the compounded annual rate. But a bank is
likely to mean the (nominal) "interest rate".
Are we talking about a US financial institution or otherwise?
A US financial institution should know to use the words "interest
rate" or "APY" (aka APR; annual percentage yield/rate). In US law,
"interest rate" specifically means the non-compounded rate (aka
nominal rate), whereas "APY" specifically means the compounded rate.
Can you explain "6% Nominal Interest for me....to ensure I understand the
term. Would that be 6% of First Year + 6% of Second Year = 6% of remaining
year fraction?.....not compounding?
It has nothing to do with year-to-year compounding or not. In US law,
interest must compound at least annually. At issue is how intra-
annual rates are computed (e.g. daily, monthly, quarterly).
Following US law, given a nominal annual rate "r" and a compounding
frequency "t", the rate per compounding period is r/t. Here, I am
using t=365 for daily [1], 52 for weekly, 12 for monthly, and 4 for
quarterly.
The APY (or APR, a deprecated term which is still used frequently) is
the annual effect (aka "effective rate") of that period compounding.
That is, if the periodic rate is r/t, the APY is (1 + r/t)^t -1, where
"^" means "to the power of" (that is, multplied by itself t times).
The Excel Analysis ToolPak does have the functions NOMINAL and
EFFECT. You can read their Help pages. (That is true for Excel 2003,
at least.) Personally, I don't use them.
Bringing this down to earth, if a bank specifies an "interest
rate" (those words have a technical meaning) of 6% with daily
compounding, then the APY is (1 + 6%)^365 - 1, which is the same as
FV(6%/365, 365, 0, -1) - 1. That is approximately 6.1831%.
Conversely, if a bank or investment institution specifies an APY of
6.1831%, that compares to a nominal "interest rate" with daily
compounding of 365 * ((1 + 6.1831%)^(1/365) - 1), which is the same as
365*RATE(365, 0, -1, 1+6.1831%). Of course, that should be 6%. (I
always use the exact result of interest calculations, not their
approximation.)
Complicating the whole thing is that (US) banks usually use an average
daily balance method to compute the periodic rate and, hence, the
APY. But that should make a difference only if the balance is
changing due to deposits and withdrawals. In your simple case, you
specified only an initial investment (or a value on a particular
date).
HTH.
Endnotes:
[1] Financial institutions have the option of using 366 for the daily
frequency in leap years. I presume that most do because it is to
their advantage. (A very-slightly lower daily rate. But remember:
large banks multiply that infinitesimal fractional difference times
thousands of accounts, some of which have 6- and 7-digit balances.)
