 141.1: Ordinary annuity $1,000 5% Annually 8
 141.2: Ordinary annuity $ 500 4% Semiannually 4
 141.3: Ordinary annuity $2,000 8% Quarterly 3
 141.4: Annuity due $3,000 6% Semiannually 3
 141.5: Annuity due $5,000 3% Annually 4
 141.6: Annuity due $ 800 7% Annually 5
 141.7: Manually find the future value of an ordinary annuity of $300 paid ...
 141.8: Manually find the future value of an annuity due of $500 paid semia...
 141.9: Find the future value of an ordinary annuity of $3,000 annually aft...
 141.10: Len and Sharron Smith are saving money for their daughter Heather t...
 141.11: Harry Taylor plans to pay an ordinary annuity of $5,000 annually fo...
 141.12: Scott Martin is planning to establish a retirement annuity. He is c...
 141.13: Pat Lechleiter pays an ordinary annuity of $2,500 quarterly at 8% a...
 141.14: Find the future value of an ordinary annuity of $6,500 semiannually...
 141.15: Latanya Brown established an ordinary annuity of $1,000 annually at...
 141.16: You invest in an ordinary annuity of $500 annually at 8% annual int...
 141.17: You invest in an ordinary annuity of $2,000 annually at 8% annual i...
 141.18: Make a chart comparing your results for Exercises 16 and 17. Use th...
 141.19: Find the future value of an annuity due of $12,000 annually for thr...
 141.20: Bernard McGhee has decided to establish an annuity due of $2,500 an...
 141.21: Find the future value of an annuity due of $7,800 annually for two ...
 141.22: Find the future value of an annuity due of $400 annually for two ye...
 141.23: Find the future value of a quarterly annuity due of $4,400 for thre...
 141.24: Find the future value of an annuity due of $750 semiannually for fo...
 141.25: Which annuity earns more interest: an annuity due of $300 quarterly...
 141.26: You have carefully examined your budget and determined that you can...
 141.27: June Watson is contributing $3,000 each year to a Roth IRA. The IRA...
 141.28: Marvin Murphy contributes $400 per month to a payroll deduction 401...
Solutions for Chapter 141: FUTURE VALUE OF AN ANNUITY
Full solutions for Business Math,  9th Edition
ISBN: 9780135108178
Solutions for Chapter 141: FUTURE VALUE OF AN ANNUITY
Get Full SolutionsThis textbook survival guide was created for the textbook: Business Math, , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Business Math, was written by and is associated to the ISBN: 9780135108178. Since 28 problems in chapter 141: FUTURE VALUE OF AN ANNUITY have been answered, more than 17286 students have viewed full stepbystep solutions from this chapter. Chapter 141: FUTURE VALUE OF AN ANNUITY includes 28 full stepbystep solutions.

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!

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Solvable system Ax = b.
The right side b is in the column space of A.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.