Simple and compound interest calculation in financial mathematics

Id e nti fication of variables

I = Value of interest in pesos.

i = Percentage interest rate.

n = Number of periods.

n / 360 = Number of periods (days).

A = Annuity

F = Future value.

P = Present value.

VT = Transaction value.

D = Discount.

Value of interest in pesos.

I = P * i * n

Note:

For Ordinary Interest (Commercial, bank) n = 360, 30 days, 12 months.

For Rational Interest (Exact or true) n = 365, 366 days, ANNUITIES SIMPLE INTEREST.

COMPOUND INTERESTS.

I = Value of interest in pesos.

in = Nominal interest rate.

ie = effective interest rate

ia = Advance interest rate.

go = real rate

F = Future value.

P = Present value.

n = Number of periods.

D = Discount in days

A = Annuity or periodic payment.

G = g = Constant variation (arithmetic gradient) or percentage variation (geometric gradient).

R = Annuity equivalent to an arithmetic gradient or a geometric gradient.

INTEREST RATES.

Periodic nominal interest rate:

CONVERSION INTEREST RATES: NOMINAL (i n) AND EFFECTIVE (i e)

ANNUITIES INTEREST COMPOUND

GRADIENT

ARITHMETIC GRADIENT.

GEOMETRIC GRADIENT.

CONTINUING INTEREST

F = Future value.

P = Present value

A = Annuity.

n = Number of periods.

r = Nominal rate over the period compounded continuously.

FINANCIAL EVALUATION OF INVESTMENT PROJECTS

PRESENT VALUE. (P)

It is the value that currently has the sum of a payment or a series of payments that will be made in future periods.

P = F (1 + i) ^-n

FUTURE VALUE. (F)

It is the future value of a payment or series of payments made in current periods.

F = P (1 + i) ⁿ

NET PRESENT VALUE:

It is the wealth or loss that an investment project creates during its useful life.

VPN = - ΣVP expenses + ΣVP income

VPN	PROJECT PROFITABILITY	MEANING OF THE VPN AS TO THE PROJECT
VPN> 0	The profitability of the project is greater than the investor's opportunity rate	The income at the opportunity rate is greater than the expenses, therefore they generate wealth for the investor.
VPN <0	The profitability of the project is less than the investor's opportunity rate	Expenses at the opportunity rate are greater than income, therefore they generate loss to the investor.
VPN = 0	The profitability of the project is equal to the investor's opportunity rate, it is called the IRR	As there is no wealth or loss for the investor, it is indifferent to place resources in the project.

INTERNAL RATE OF RETURN. (TIR)

It is defined as the profitability of the resources invested or reinvested during the life of an investment project and are equivalent to the intertemporal discount rate that makes the net present value equal to zero.

TIR	PROJECT PROFITABILITY	MEANING OF THE IRR AS TO THE PROJECT
IRR> ip	The profitability of the project is greater than the investor's opportunity rate	It is the profitability produced by the investor, the project against the opportunity rate.
IRR <ip	The profitability of the project is less than the investor's opportunity rate	It is the lowest profitability that the project produces for the investor, if it is carried out.
IRR = ip	The profitability of the project is equal to the investor's opportunity rate	It does not generate a higher profitability for the investor, the project would be indifferent.

INTERNAL RATE OF RETURN ADJUSTED.

It is defined as the rate resulting from using the capital cost rate in the flows of a project, calculated as follows:

ANNUAL EQUIVALENT ANNUAL VALUE / ANNUAL EQUIVALENT ANNUAL COST.

It consists of transforming a cost and income structure into a uniform series of installments over time. The VPN is part of a project.

BENEFIT / COST REASON .

Proof that you weigh the benefits and costs of a project, especially a public one, in terms of its contribution to well-being or economic development.

SYMBOLOGY:

P = VP: Present value or current value.

F = VF: Future value or amount.

n: Period of time.

i = ip: interest rate or opportunity interest rate.

DAY TABLE

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