- 13-1.1: A loan of $5,000 at 6% compounded semiannually for two years
- 13-1.2: A loan of $18,500 at 6% compounded quarterly for four years
- 13-1.3: An investment of $7,000 at 2% compounded semiannually for six years
- 13-1.4: A loan of $500 at 5% compounded semiannually for five years
- 13-1.5: A loan of $1,000 at 12% compounded monthly for two years
- 13-1.6: An investment of $2,000 at 1.5% compounded annually for ten years
- 13-1.7: Thayer Farm Trust made a farmer a loan of $1,200 at 16% for three y...
- 13-1.8: Maeola Killebrew invests $3,800 at 2% compounded semiannually for t...
- 13-1.9: Carolyn Smith borrowed $6,300 at for three years compounded annuall...
- 13-1.10: Margaret Hillman invested $5,000 at 1.8% compounded quarterly for o...
- 13-1.11: First State Bank loaned Doug Morgan $2,000 for four years compounde...
- 13-1.12: A loan of $8,000 for two acres of woodland is compounded quarterly ...
- 13-1.13: Compute the compound amount and the interest on a loan of $10,500 c...
- 13-1.14: Find the future value of an investment of $10,500 if it is invested...
- 13-1.15: You have $8,000 that you plan to invest in a compoundinterest- bear...
- 13-1.16: Find the future value of $50,000 at 6% compounded semiannually for ...
- 13-1.17: Find the effective interest rate for a loan for four years compound...
- 13-1.18: What is the effective interest rate for a loan of $5,000 at 10% com...
- 13-1.19: Ross Land has a loan of $8,500 compounded quarterly for four years ...
- 13-1.20: What is the effective interest rate for a loan of $20,000 for three...
- 13-1.21: Find the compound interest on $2,500 at 0.75% compounded daily by L...
- 13-1.22: How much compound interest is earned on a deposit of $1,500 at 0.5%...
- 13-1.23: John McCormick has found a short-term investment opportunity. He ca...
- 13-1.24: What is the compound interest on $8,000 invested at 1.25% for 180 d...
Solutions for Chapter 13-1: COMPOUND INTEREST AND FUTURE VALUE
Full solutions for Business Math, | 9th Edition
Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or - sign.
Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.
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 IIA-1 yll2 = Y T(AAT)-1 Y = 1 displayed by eigshow; axis lengths ad
Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.
Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.
Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.
Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.
Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = 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.
Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A - AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).
If N NT = NT N, then N has orthonormal (complex) eigenvectors.
Every v in V is orthogonal to every w in W.
The diagonal entry (first nonzero) at the time when a row is used in elimination.
Rank r (A)
= number of pivots = dimension of column space = dimension of row space.
Similar matrices A and B.
Every B = M-I AM has the same eigenvalues as A.
Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!
Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.
Constant down each diagonal = time-invariant (shift-invariant) filter.
Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.
Tridiagonal matrix T: tij = 0 if Ii - j I > 1.
T- 1 has rank 1 above and below diagonal.