 5.70.26: In 2326, find the effective rate of interest.
 5.70.27: In 2730, determine the rate that represents the better deal
 5.70.28: In 2730, determine the rate that represents the better deal
 5.70.29: In 2730, determine the rate that represents the better deal
 5.70.30: In 2730, determine the rate that represents the better deal
 5.70.31: What rate of interest compounded annually is required to double an ...
 5.70.32: What rate of interest compounded annually is required to double an ...
 5.70.33: What rate of interest compounded annually is required to triple an ...
 5.70.34: What rate of interest compounded annually is required to triple an ...
 5.70.35: (a) How long does it take for an investment to double in value if i...
 5.70.36: (a) How long does it take for an investment to triple in value if i...
 5.70.37: What rate of interest compounded quarterly will yield an effective ...
 5.70.38: What rate of interest compounded continuously will yield an effecti...
 5.70.39: If Tanisha has $100 to invest at 8% per annum compounded monthly, h...
 5.70.40: If Angela has $100 to invest at 10% per annum compounded monthly, h...
 5.70.41: How many years will it take for an initial investment of $10,000 to...
 5.70.42: How many years will it take for an initial investment of $25,000 to...
 5.70.43: What will a $90,000 condominium cost 5 years from now if the price ...
 5.70.44: A department store charges 1.25% per month on the unpaid balance fo...
 5.70.45: Jerome will be buying a used car for $15,000 in 3 years. How much m...
 5.70.46: John requires $3000 in 6 months to pay off a loan that has no prepa...
 5.70.47: George contemplates the purchase of 100 shares of a stock selling f...
 5.70.48: A business purchased for $650,000 in 2005 is sold in 2008 for $850,...
 5.70.49: Jim places $1000 in a bank account that pays 5.6% compounded contin...
 5.70.50: On January 1, Kim places $1000 in a certificate of deposit that pay...
 5.70.51: Will invests $2000 in his IRA in a bond trust that pays 9% interest...
 5.70.52: Suppose that April has access to an investment that will pay 10% in...
 5.70.53: The average annual cost of college at 4year private colleges was $...
 5.70.54: Colleen and Bill have just purchased a house for $650,000, with the...
 5.70.55: In February 2009, President Obama signed into law a $787 billion fe...
 5.70.56: In 2011, the federal debt was about $14 trillion. In 2011, the U.S....
 5.70.57: If the inflation rate averages 3%, how much will $1000 purchase in ...
 5.70.58: If the inflation rate averages 2%, how much will $1000 purchase in ...
 5.70.59: If the amount that $1000 will purchase is only $950 after 2 years, ...
 5.70.60: If the amount that $1000 will purchase is only $930 after 2 years, ...
 5.70.61: If the average inflation rate is 2%, how long is it until purchasin...
 5.70.62: If the average inflation rate is 4%, how long is it until purchasin...
 5.70.63: A zerocoupon bond can be redeemed in 20 years for $10,000. How muc...
 5.70.64: A childs grandparents are considering buying a $40,000 facevalue, ...
 5.70.65: How much should a $10,000 facevalue, zerocoupon bond, maturing in ...
 5.70.66: If Pat pays $12,485.52 for a $25,000 facevalue, zerocoupon bond t...
 5.70.67: The formula t = ln m n lna1 + r n b
 5.70.68: The formula t = ln A  ln P r can be used to find the number of yea...
 5.70.69: (a) The CPI was 163.0 for 1998 and 215.3 for 2008. Assuming that an...
 5.70.70: If the current CPI is 234.2 and the average annual inflation rate i...
 5.70.71: If the average annual inflation rate is 3.1%, how long will it take...
 5.70.72: The base period for the CPI changed in 1998. Under the previous wei...
 5.70.73: Explain in your own words what the term compound interest means. Wh...
 5.70.74: Explain in your own words the meaning of present value
 5.70.75: You have just contracted to buy a house and will seek financing in ...
Solutions for Chapter 5.70: Financial Models
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 5.70: Financial Models
Get Full SolutionsChapter 5.70: Financial Models includes 50 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. Since 50 problems in chapter 5.70: Financial Models have been answered, more than 59319 students have viewed full stepbystep solutions from this chapter. 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.

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!

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

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

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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

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.

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.