In order to compare the results obtained by the different methods of calculating interest, let us take the example of a contract for \$5,000 dated January 1 and payable in monthly instalments of \$100 each, interest being charged each half-year at the rate of 6% per annum on the balances remaining unpaid from time to time. Let us suppose the \$100 is paid on each of the following dates:

January 30 February 15 March 15 April 10

May 20 June 30 July 30 August 15

September 15 October 10 November 20 December 31

If interest is calculated when each payment is made, the figures will be as follows:

 Jan. I Principal............................... \$5,000.00 June 30 Deduct six payments............................... 600.00 \$4,400.00 Add interest on \$5,000.................................. \$150.00 Less interest on \$100 for: 5 mos. 0 days (Jan. 30 to June 30) 4 " 15 " Feb. 15 " " ,, 3 " 15 ,, Mar. 15 ,, ,, ,, 2 " 20 " Apr. 10 ,, " " 1 " 10 " May 20 " " " 17 mos.................................................................. 8.50 141.50 \$4,541.50 Dec. 31 Deduct six payments...................................................... 600.00 \$3,941.50
 Add interest: For six months on \$4,541.50 at 6%...... \$136.24 Less interest on payments as above.. 8.50 127.74 Balance at end of year........................................ \$3,813.76

If the interest is calculated on the balances remaining unpaid at the end of each half-year, the result will be:

 Jan. 1 Principal due,.................................. \$5,000.00 June 30 Deduct six payments.............................. 600.00 \$4,400.00 Add interest for six months on \$4,400 at 6%...... 132.00 \$4,532.00 Dec. 31 Deduct six payments........................... 600.00 \$3,932.00 Add interest for six months on \$3,932 at 6%..... 117.96 Balance at end of the year................ \$4,049.96

If no payments are made, the figures would be:

 Jan. 1 Principal......................... \$5,000.00 June 30 Interest for six months,................... 150.00 \$5,150.00 Dec. 31 Interest for six months...................... I54.50 Balance at end of the year................ \$5,30450

Here the interest is compounded, which, under the laws of some states, is illegal. In such cases, the proper calculation, figuring simple interest, would be as follows:

 Jan. 1 Principal........................................ \$5,000.00 June 30 Interest for six months......................... 150.00 Dec. 31 Interest for six months............................. 150.00 Balance at end of the year.............................. \$5,300.00

If interest is charged on the "average balances," the figures would be as follows:

 Jan. 1 Principal................................ \$5,000.00 June 30 Deduct six payments............................... 600.00 \$4,400.00 Add interest on balance of March 31, viz.: \$4,700 141.00 \$4,541.00 Dec. 31 Deduct six payments.............................. 600.00 \$3,041.00 Add interest on balance of September 30, viz.: \$4,241..................................... 127.23 Balance at end of the year.................................... \$4,068.23

It must be remembered that, in all the examples, the differences will rapidly increase as time progresses.