The Simple Interests Mode
In order to understand Simple Interest Mode you have to keep in mind the key word "proportions".
The concept of proportion
Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this result the principles of symmetry. Without symmetry and proportion there can be no principles in the design of any temple; that is, if there is no precise relation between its members as in the case of those of a well shaped man. —Vitruvius,[1] The Ten Books of Architecture (III, Ch. 1)
Definition
The definition of a vector space requires a field F such as the field of rational, real or complex numbers. A vector space is a set V together with two operations that combine two elements to a third:
vector addition: any two vectors, i.e., elements of V, v and w can be added to yield a third vector v + w
scalar multiplication: any vector can be "scaled": multiplied by a scalar, an element of F. The product of a vector v and scalar a is denoted av.
To specify the field F, one speaks of an F-vector space or a vector space over F. For F = R or C, they are also called real and complex vector spaces, respectively. To qualify as a vector space, addition and multiplication have to adhere to a number of requirements called axioms generalizing the situation of Euclidean plane R2 or Euclidean space R3.[1] For distinction, vectors v will be denoted in boldface.[nb 2] In the formulation of the axioms below, let u, v, w be arbitrary vectors in V, and a, b be scalars, respectively.
Axiom
Signification
Associativity of addition
u + (v + w) = (u + v) + w
Commutativity of addition
v + w = w + v
Identity element of addition
There exists an element 0 ∈ V, called the zero vector, such that v + 0 = v for all v ∈ V.
Inverse elements of addition
For all v ∈ V, there exists an element w ∈ V, called the additive inverse of v, such that v + w = 0. The additive inverse is also denoted −v.
Distributivity of scalar multiplication with respect to vector addition
a(v + w) = av + aw
Distributivity of scalar multiplication with respect to field addition
(a + b)v = av + bv
Compatibility of scalar multiplication with field multiplication
a(bv) = (ab)v [nb 3]
Identity element of scalar multiplication
1v = v, where 1 denotes the multiplicative identity in F
The space V = R2 over the real numbers, with the addition and multiplication as above, is indeed a vector space. Checking the axioms reduces to verifying simple identities such as
(x, y) + (0, 0) = (x, y),
so that (0, 0) is the zero vector of V. The distributive law amounts to
(a + b) · (x, y) = a · (x, y) + b · (x, y).
In contrast to the intuition stemming from R2 and higher-dimensional cases, there is, in general vector spaces, no notion of nearness, angles or distances. To deal with such matters, particular types of vector spaces are introduced; see below.
The Simple Interest (SMPL) Mode lets you calculate the interest amount and/or simple future value (principal and interest amount).
Entering the SMPL Mode
Press SMPL
Setting values
No.DisplayNameValues Usedin Examples®Set*Days in Year (Date Mode)365®DysNumber of Interest Periods (Number of Days)120®1%Interest Rate (Annual)5%®PVPrincipal (Present Value)$10,000
C Basic SMPL Mode Procedure
Example 1: To calculate the interest amount (SI), and the simple future value (SFV)
Example 2: To calculate the simple interest (SI) amount only
Example 3: To calculate the simple future value (SFV) only
C SMPL Mode Financial Calculation Variables (VARS)• Variables Dys, 1%, and PV are used in the SMPL Mode.• The values of SMPL Mode variables are retained even if you change to another mode. Note, however, that SMPL Mode variables are also used by other modes, so performing an input or calculation operation may change the values assigned to them.•Though SMPL Mode variables are financial calculation variables, they are also used by arithmetic and function operations in the COMP Mode.
C Calculation FormulasDys 1%365-day Mode SI = PVxi (i=360-day Mode 2.!>< i ="SFV">
Casio FC-200V - SMPL Mode
