Highways and Highway Transportation

by George R. Chatburn

= 3.363572

Annual Payment = Log^-1 3.363571 = $2309.748.

The following table shows the repayment of the loan by annual payments of $2309.75:

Year	Principal Owing at Beginning of Year	Interest for Year	Principal Repaid at End of Year	Total Payment for Year
1	$10,000.00	$500.00	$1,809.75	$2,309.75
2	8,190.25	409.51	1,900.24	2,309.75
3	6,290.01	314.50	1,995.25	2,309.75
4	4,294.76	214.74	2,095.01	2,309.75
5	2,199.85	109.99	2,199.75	2,309.74
	Totals	$1548.74	$10,000.00	$11,548.74

Since it is more convenient to have the bonds in even hundreds of dollars and the interest in dollars some adjustment from the theoretical amounts are usually made but such that the annual payments will be near the theoretical. Sometimes, too, the bonds are made smaller for the first few years then gradually increase so that the natural growth in population and wealth may bear its proportional burden. One adjustment for the example just given is shown:

Year	Principal Owing at Beginning of Year	Interest for Year	Principal Repaid at end of Year	Total Payment for Year
1	$10,000	$500	$1,800	$2,300
2	8,200	410	1,900	2,310
3	6,300	315	2,000	2,315
4	4,300	215	2,100	2,315
5	2,000	100	2,000	2,100
	Totals	$1,500	$10,000	$11,550

Total Cost by the Three Kinds of Bonds.

—The total cost of a loan, as shown by the following table taken from Bulletin 136, U. S. Department of Agriculture, is generally greatest under the sinking fund plan and least under the serial. The serial, too, is the simplest to compute.

Total Cost of a $100,000 Loan for 20 Years
Interest Compounded Annually[198]

Annual Interest on Bonds		Sinking-fund Bond Compounded Annually at			Annuity Bond	Serial Bond
		3%	31⁄2%	4%
4		$154,431	$150,722	$147,163	$147,163	$142,000
4	1⁄2	164,431	160,722	157,163	153,752	147,250
5		174,431	170,722	167,163	160,485	152,500
5	1⁄2	184,431	180,722	177,163	167,359	157,750
6		194,431	190,722	187,163	174,369	163,000