 13.1: Use Table 131 or the appropriate formula for Exercises 14.
 13.2: Use Table 131 or the appropriate formula for Exercises 14.
 13.3: Use Table 131 or the appropriate formula for Exercises 14.
 13.4: Use Table 131 or the appropriate formula for Exercises 14.
 13.5: Find the amount that should be set aside today to yield the desired...
 13.6: Find the amount that should be set aside today to yield the desired...
 13.7: Find the amount that should be set aside today to yield the desired...
 13.8: Find the amount that should be set aside today to yield the desired...
 13.9: Manually calculate the compound interest on a loan of $1,000 at 8%,...
 13.10: Manually calculate the compound interest on a 13% loan of $1,600 fo...
 13.11: Use Table 131 or the appropriate formula to find the future value ...
 13.12: Use Table 131 or the appropriate formula to find the interest on a...
 13.13: Find the future value of an investment of $8,000 compounded quarter...
 13.14: Find the compound interest on a loan of $5,000 for two years if the...
 13.15: Mario Piazza was offered $900 now for one of his salon photographs ...
 13.16: Lauren McAnally invests $2,000 at 2% compounded semiannually for tw...
 13.17: Use Table 132 to find the compound interest and the compound amoun...
 13.18: Use Table 132 to find the amount of interest on $100 invested for ...
 13.19: $1,500 in three years at 2.5% compounded annually
 13.20: $1,000 in seven years at 8% compounded quarterly
 13.21: $4,000 in two years at 2% annual interest compounded quarterly
 13.22: $500 in 15 years at 4% annual interest compounded semiannually
 13.23: Find the amount that should be invested today to have $1,800 in one...
 13.24: Myrna Lewis wishes to have $4,000 in four years to tour Europe. How...
Solutions for Chapter 13: COMPOUND INTEREST, FUTURE VALUE, AND PRESENT VALUE
Full solutions for Business Math,  9th Edition
ISBN: 9780135108178
Solutions for Chapter 13: COMPOUND INTEREST, FUTURE VALUE, AND PRESENT VALUE
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Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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.

Column space C (A) =
space of all combinations of the columns of A.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Outer product uv T
= column times row = rank one matrix.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).