Reference to good annuity tables* will usually solve the questions which arise in connection with instalment mortgages, i.e.: being given the purchase price and the rate of interest -

* Stubbins' Annuity Tables will be found advantageous in this connection from the fact that they show monthly payments - something which few, if any, of the other tables do.

1. How many payments of a stated sum are necessary to liquidate principal and interest? Or,

2. The number of payments being agreed upon, what should be the amount of each payment?

As a rule, a concern sells on a fairly uniform basis. For instance, it will accept in payment for sales, say, 120 monthly payments of $11.12 each, for each $1,000 of purchase money with interest at 6% per annum. In such cases a table can easily be constructed showing the division of each payment into principal and interest, so that at any time the amount of principal paid in can be determined.

For example, reference to the table shows that 120 monthly payments of $11.12 will pay off a principal debt of $1,000 with interest at 6% per annum. The interest for the first month on $1,000 is $5, and the principal included in the first payment is therefore: $11.12 - $5.00 = $6.12. The interest for the second month is to be computed on $1,000 - $6.12 = $993.88, and amounts to $4.97; the principal included in the second payment is therefore: $11.12 - $4.97 = $6.15.

The rule for the construction of such tables is as follows: Having found the amount of principal contained in the first payment, multiply this by 1 plus the ratio of interest for one month. At the rate of 6% per annum, the monthly rate would be .005. If the principal part of the first payment is $6.12, the amount of the principal in the second payment will be found by multiplying this amount by 1.005, the same process being repeated until the table is completed.

The amount of principal included in any given number of payments may also be found by reference to annuity tables or by algebra, these amounts being in geometric progression. The table will appear as follows:

Principal Unpaid

Payment

Amount

Interest

Principal

1

$11.12

$5.oo

$6.12

$993.88

2

11.12

4.97

6.15

987.73

3

11.12

4.94

6.18

981.55

4

11.12

4.91

6.21

975.34

5

11.12

4.88

6.24

969.10