 11.6.11.1.258: An account into which, or out of which, a sequence of scheduled pay...
 11.6.11.1.259: The amount of money that is present in an ordinary annuity after t ...
 11.6.11.1.260: A type of annuity in which the goal is to save a specific amount of...
 11.6.11.1.261: A variable annuity is an annuity that is invested in stocks, bonds,...
 11.6.11.1.262: An annuity that is established with a lump sum for the purpose of p...
 11.6.11.1.263: Accounts where individuals may invest up to a certain amount of mon...
 11.6.11.1.264: A retirement savings plan where employees of private companies can ...
 11.6.11.1.265: A retirement plan similar to a 401k plan, but available only to emp...
 11.6.11.1.266: In Exercises 912, use the ordinary annuity formula A = pc a1 + r n ...
 11.6.11.1.267: In Exercises 912, use the ordinary annuity formula A = pc a1 + r n ...
 11.6.11.1.268: In Exercises 912, use the ordinary annuity formula A = pc a1 + r n ...
 11.6.11.1.269: In Exercises 912, use the ordinary annuity formula A = pc a1 + r n ...
 11.6.11.1.270: In Exercises 1316, use the sinking fund formula p = Aa r n b a1 + r...
 11.6.11.1.271: In Exercises 1316, use the sinking fund formula p = Aa r n b a1 + r...
 11.6.11.1.272: In Exercises 1316, use the sinking fund formula p = Aa r n b a1 + r...
 11.6.11.1.273: In Exercises 1316, use the sinking fund formula p = Aa r n b a1 + r...
 11.6.11.1.274: In Exercises 1720, round all answers to the nearest cent.Retirement...
 11.6.11.1.275: In Exercises 1720, round all answers to the nearest cent.Starting a...
 11.6.11.1.276: In Exercises 1720, round all answers to the nearest cent.Saving for...
 11.6.11.1.277: In Exercises 1720, round all answers to the nearest cent.Grandchild...
 11.6.11.1.278: In Exercises 2124, round all answers up to the next cent.Saving for...
 11.6.11.1.279: In Exercises 2124, round all answers up to the next cent.Campaign F...
 11.6.11.1.280: In Exercises 2124, round all answers up to the next cent.Becoming a...
 11.6.11.1.281: In Exercises 2124, round all answers up to the next cent.Repaying a...
 11.6.11.1.282: Dont Wait to Invest The purpose of this exercise is to demonstrate ...
 11.6.11.1.283: Investing in Stocks Using the Internet, financial magazines, books,...
 11.6.11.1.284: Investing in Bonds Using the Internet, financial magazines, books, ...
 11.6.11.1.285: Investing in Mutual Funds Using the Internet, financial magazines, ...
 11.6.11.1.286: Financial Advisor Interview Annuities, IRAs, 401k plans, 403b plans...
Solutions for Chapter 11.6: Consumer Mathematics
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 11.6: Consumer Mathematics
Get Full SolutionsChapter 11.6: Consumer Mathematics includes 29 full stepbystep solutions. Since 29 problems in chapter 11.6: Consumer Mathematics have been answered, more than 79972 students have viewed full stepbystep solutions from this chapter. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665. This textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.