Reading Numbers

An interesting aspect of financial calculations is becoming familiar with
the formulas involved, effectively learning to 'read' them. What is the source
of the difficulty, giving us such apparently complex formulas? The quite simple fact
that .95 * 105 does not give 100. It gives 99.75. Because the reference number is now
larger than 100 ie 105. If I pay back ù 100$ at 5% after one year - 105$ - the percentage
of capital in the payment will be more than 95:

And the percentage of interest less than 5. For a loan being repaid monthly, this
situation will also hold.

Working with the problem of a 1000$ loan at 5% repaid over one year, let's

examine the meaning of the numbers.

0.004167                             5% over 12 months, per month

1.004167                             a factor; adding interest to capital

(1.004167)^12 =                 above factor, iterated 12 times ( one year)

1.0512

1/1.0512 =                          the reciprocal; represents the capital part of payment
0.9513

1 - 0.9513
0.04867                               the interest part of amount due for 1 month

The formula multiples the loan amount by the monthly interest rate, giving 4.17.
This is divided by the interest factor on the payment amount. The payment should be
85.68$ per month. (This should also be the last payment!!)

The first interest payment corresponds to a .0512 interest rate with respect to that
payment amount. The last - at 0.36 - to one of .0014617. One can check all those
in between using (1.004167)^11, (1.004167)^10 ... etc.