There are three methods of calculating this "unearned" interest:
1. By a rough averaging of the time, i.e., the life, of the mortgage.
2. By reference to tables.
3. By mathematical calculation.
The first is a rough-and-ready plan which is frequently adopted but which is not accurate. It is based upon an average of the interest, and, instead of charging interest at the nominal rate for the entire period, it is charged at that rate for one-half the period, and this amount is added to the principal. The sum is then divided by the number of payments to be made.
For example, what would be the amount of each monthly payment in order to pay off $1,000 in ten years, interest at 6% ?
The simple interest for half the period, i.e., 5 years at 6% per annum = 30% of the principal; the number of payments is 120.
30% of $1,000 = $300 $1,000 + $300 / 120 = $10.833, the monthly payment
For the second method, there are published numerous tables showing present values of annuities, and most of the problems occurring in practice may be solved by their use. As rules are always attached to each set of such tables, showing the manner of using them, this need not be discussed here. Most tables in use, however, are based on quarterly, half-yearly, or annual payments, and it is frequently necessary to base calculations upon monthly payments, in which case special tables must be used.* Before tables can be used we must know whether the interest is to be charged half-yearly or monthly, and if the latter, whether each monthly payment is to be made on the first or the last day of each month.
The third method of determining the monthly payments by mathematical calculation involves the use of complicated formulae, and sometimes logarithms - matters beyond the scope of the present work. The results obtained coincide with those given by any reliable tables; but by means of formulae it is, of course, possible to answer any question which may arise, whereas the tables can only be used for those questions in which occur certain definite periods.
Taking the example just given, the tables or the mathematical calculations give us the following results:
If interest be reckoned on half-yearly balances, ignoring the fact that a payment has been made each month......................................
If each payment be made on the last of the month, and interest be allowed thereon. . . .
If payments be made on the first of each month, and interest be allowed thereon.....................
It will be seen that, by using different methods the results may vary as much as 39 cents on each payment (i.e., $11.23 - $10.84), or a total of $46.80 on the principal. If real estate dealers realized more fully the existence and amount of these differences, they would undoubtedly take the necessary trouble to have accurate calculations made. As a matter of fact, under the first method, the seller does not receive the percentage which he thinks he is getting, i.e., 6% in the instance given.
*See Stubbing' "Tables of Present Value of Annuities," an English work.