Interest

If a person borrows money, he usually pays something for the loan.

The sum of money he borrows is called the Principal; the money he pays for the use of the principal is called Interest. Interest is generally reckoned at so much for the use of each $100 for one year. This amount is called the Rate per cent per Annum.

Thus, if we say that $200 is borrowed for three years at 4 per cent per annum, we mean that the borrower, at the end of each year, pays the lender $4 for each $100 borrowed—i.e., $8 interest for each year.

In the above example the interest is supposed to be paid to the lender at the end of each year. Interest thus reckoned is called Simple Interest.

The sum obtained by adding the interest for any given time to the principal is called the Amount in that time.

Common Interest Methods

If we were to find the interest on a sum of money for 3 years 4 months 5 days, we would find the interest for 1 year, then for 1 month (¹⁄₁₂ of a year), then for 1 day (¹⁄₃₆₀ of a year). Having the interest for 1 year 1 month 1 day, it is a simple matter of multiplication to get it for 3 years 4 months 5 days.

Example:

What is the interest on $520 for 1 year 3 months at 6%?

Work:
1 year 3 months = 1¹⁄₄ year
		$520	principal
		.06
4	)	$31.20	interest	1		year
		$7.80	interest		¹⁄₄	year
		$39.00	interest	1	¹⁄₄	year

The 60-Day Interest Method

In what is called the 60-Day Method, 360 days are considered one year, and 30 days one month. Upon this basis the interest for 60 days, or two months, at any rate, will be ¹⁄₆ of the interest for one year; and when the rate is 6% the interest for 60 days is one per cent or ¹⁄₁₀₀ of the principal. Thus, the interest of $247 for 60 days at 6% is $2.47.

Example: Find the interest of $1728 for 80 days at 6%.

Work:

$17	28	= interest for 60 days.
5	76	= interest for 20 days.
$23	04	= interest for 80 days.

Explanation:

The interest of $1728 for 60 days at 6% is 1% of $1728, or $17.28; and the interest for 20 days (¹⁄₃ of 60) is ¹⁄₃ of $17.28, or $5.76. Hence for 80 days it will be $17.28 plus $5.76, or $23.04.

Methods of Reckoning Time

The Common Method.—When the time is long, generally 30 days are considered a month.

The Exact Method.—When the time is short, the exact number of days is generally counted but we sometimes find the exact number of days also when the time is long.

The Bankers’ Method.—Bankers get the exact number of days between two dates, but each day is reckoned as ¹⁄₃₆₀ of a year.

Problem, when the time is long.

Find the time between April 12, 1895, and September 22, 1899.

Best Method

From April 12, 1895, to April 12, 1899, is 4 years.
From April 12, 1899, to Sept. 12, 1899, is 5 months.
From Sept. 12, 1899, to Sept. 22, 1899, is 10 days.
Time between dates = 4 years 5 months 10 days.

Another Method

1899	9	22
1895	4	12
4	5	10

Problem, when the time is short. Find the difference in time between April 12 and July 15, 1902.

Work:

Number of days left	in April	=	18
	in May	=	31
	in June	=	30
	in July	=	15
Total number of days		=	94

Note.—If the rate and principal are given, it is a simple matter to find the interest, now that we have the time.

Example of the use of Table: What is the time from February 10 to October 18, in the same year. February 10 is numbered 41, and October 18 is numbered 291; 291 - 41 = 250, Ans. This includes the last day, but not the first. If both days are taken, subtract 40 from 291 = 251, Ans. When February 29 occurs in a term, count an additional day. The day of the date of a note is not included in its term; thus, required the last day of grace of a note dated March 24, at 90 days. March 24 = 83; 83 + 93 = 176 = June 25, Ans.

TABLE OF TIME, IN DAYS
The following table gives the exact time, in days, between two dates.

Jan.	Feb.	March	April	May	June	July	Aug.	Sept.	Oct.	Nov.	Dec.
1	32	60	91	121	152	182	213	244	274	305	335
2	33	61	92	122	153	183	214	245	275	306	336
3	34	62	93	123	154	184	215	246	276	307	337
4	35	63	94	124	155	185	216	247	277	308	338
5	36	64	95	125	156	186	217	248	278	309	339
6	37	65	96	126	157	187	218	249	279	310	340
7	38	66	97	127	158	188	219	250	280	311	341
8	39	67	98	128	159	189	220	251	281	312	342
9	40	68	99	129	160	190	221	252	282	313	343
10	41	69	100	130	161	191	222	253	283	314	344
11	42	70	101	131	162	192	223	254	284	315	345
12	43	71	102	132	163	193	224	255	285	316	346
13	44	72	103	133	164	194	225	256	286	317	347
14	45	73	104	134	165	195	226	257	287	318	348
15	46	74	105	135	166	196	227	258	288	319	349
16	47	75	106	136	167	197	228	259	289	320	350
17	48	76	107	137	168	198	229	260	290	321	351
18	49	77	108	138	169	199	230	261	291	322	352
19	50	78	109	139	170	200	231	262	292	323	353
20	51	79	110	140	171	201	232	263	293	324	354
21	52	80	111	141	172	202	233	264	294	325	355
22	53	81	112	142	173	203	234	265	295	326	356
23	54	82	113	143	174	204	235	266	296	327	357
24	55	83	114	144	175	205	236	267	297	328	358
25	56	84	115	145	176	206	237	268	298	329	359
26	57	85	116	146	177	207	238	269	299	330	360
27	58	86	117	147	178	208	239	270	300	331	361
28	59	87	118	148	179	209	240	271	301	332	362
29	—	88	119	149	180	210	241	272	302	333	363
30	—	89	120	150	181	211	242	273	303	334	364
31	—	90	—	151	—	212	243	—	304	—	365

Compound Interest

Interest computed, at regular intervals, on the sum of the principal and any unpaid interest, is called compound interest. In other words, as soon as interest becomes due and is unpaid, it begins to draw interest at the same rate as the principal. Compound interest is generally paid on the deposits in savings banks and is used in calculating amortization and sinking funds.

Interest may be compounded quarterly, semi-annually, annually, or at the end of any other period agreed upon. In some States the collection of compound interest is not permitted.

Example: Find the amount and the compound interest of $1200 at 6% for two years, interest compounded semi-annually.

Solution:
$1200.	00	First principal
36.		Interest for 6 months
1236.		Principal at beginning of second 6 months
37.	08	Interest for second 6 months
1273.	08	Principal at beginning of third period
38.	19	Interest for third period
1311.	27	Principal at beginning of fourth period
39.	34	Interest for fourth period
$1350.	61	Amount at end of two years
$1350.	61	Amount at end of two years
1200.	00	Principal
150.	61	Compound interest.

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