Finite Mathematics & Its Applications (12th Edition)
12th Edition
ISBN: 9780134437767
Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
Publisher: PEARSON
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Chapter 10, Problem 34RE
To determine
To prove: The effective mortgage interest is 6%, where loan amount is
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Exercises
Evaluate the following limits.
1. lim cot x/ln x
+01x
2. lim x² In x
+014
3. lim x*
x0+
4. lim (cos√√x)1/x
+014
5. lim x2/(1-cos x)
x10
6. lim e*/*
818
7. lim (secx - tan x)
x-x/2-
8. lim [1+(3/x)]*
x→∞0
In Exercises 1 through 3, let xo =
O and calculate P7(x) and R7(x).
1. f(x)=sin x, x in R.
2. f(x) = cos x, x in R.
3. f(x) = In(1+x), x≥0.
4. In Exercises 1, 2, and 3, for |x| 1, calculate a value of n such that P(x)
approximates f(x) to within 10-6.
5. Let (an)neN be a sequence of positive real numbers such that L =
lim (an+1/an) exists in R. If L < 1, show that an → 0. [Hint: Let
1111
L
iation
7. Let f be continuous on [a, b] and differentiable on (a, b). If lim f'(x)
xia
exists in R, show that f is differentiable at a and f'(a) = lim f'(x). A
similar result holds for b.
x-a
8. In reference to Corollary 5.4, give an example of a uniformly continuous
function on [0, 1] that is differentiable on (0, 1] but whose derivative is not
bounded there.
9. Recall that a fixed point of a function f is a point c such that f(c) = c.
(a) Show that if f is differentiable on R and f'(x)| x if x 1 and hence In(1+x) 0.
12. For 0 л/2. (Thus,
as x л/2 from the left, cos x is never large enough for x+cosx to be
greater than л/2 and cot x is never small enough for x + cot x to be less
than x/2.)
Chapter 10 Solutions
Finite Mathematics & Its Applications (12th Edition)
Ch. 10.1 - Solution can be found following the section...Ch. 10.1 - Solution can be found following the section...Ch. 10.1 - Calculate the future amount of $2000 after 6...Ch. 10.1 - In Exercises 1–6, given the values of i and n...Ch. 10.1 - In Exercises 1–6, given the values of i and n...Ch. 10.1 - In Exercises 1–6, given the values of i and n...Ch. 10.1 - In Exercises 16, given the values of i and n under...Ch. 10.1 - In Exercises 16, given the values of i and n under...Ch. 10.1 - In Exercises 1–6, given the values of i and n...Ch. 10.1 - In Exercises 712, given the values of i, n, P, and...
Ch. 10.1 - In Exercises 712, given the values of i, n, P, and...Ch. 10.1 - In Exercises 7–12, given the values of i, n, P,...Ch. 10.1 - In Exercises 7–12, given the values of i, n, P,...Ch. 10.1 - Prob. 11ECh. 10.1 - In Exercises 712, given the values of i, n, P, and...Ch. 10.1 - In Exercises 1338, solve each problem. Future...Ch. 10.1 - In Exercises 1338, solve each problem. Future...Ch. 10.1 - In Exercises 1338, solve each problem. Future...Ch. 10.1 - In Exercises 13–38, solve each problem.
16. Future...Ch. 10.1 - In Exercises 1338, solve each problem. Future...Ch. 10.1 - Prob. 18ECh. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 1338, solve each problem. Present...Ch. 10.1 - In Exercises 1338, solve each problem. Savings...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 1338, solve each problem. Comparing...Ch. 10.1 - In Exercises 1338, solve each problem. Comparing...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - Prob. 27ECh. 10.1 - In Exercises 1338, solve each problem. Interest If...Ch. 10.1 - Prob. 29ECh. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 1338, solve each problem. Interest If...Ch. 10.1 - In Exercises 1338, solve each problem. Interest If...Ch. 10.1 - In Exercises 1338, solve each problem. Savings...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 13–38, solve each...Ch. 10.1 - In Exercises 1338, solve each problem. Interest...Ch. 10.1 - In Exercises 1338, solve each problem. Savings...Ch. 10.1 - In Exercises 1338, solve each problem. Savings...Ch. 10.1 - Exercises 39–52 concern simple...Ch. 10.1 - Exercises 39–52 concern simple...Ch. 10.1 - Exercises 3952 concern simple interest. Future...Ch. 10.1 - Exercises 39–52 concern simple...Ch. 10.1 - Exercises 39–52 concern simple...Ch. 10.1 - Exercises 3952 concern simple interest. Present...Ch. 10.1 - Exercises 3952 concern simple interest. Interest...Ch. 10.1 - Exercises 3952 concern simple interest. Interest...Ch. 10.1 - Exercises 3952 concern simple interest. Time...Ch. 10.1 - Exercises 3952 concern simple interest. Time...Ch. 10.1 - Exercises 3952 concern simple interest. Time...Ch. 10.1 - Exercises 3952 concern simple interest. Interest...Ch. 10.1 - Exercises 3952 concern simple interest. Present...Ch. 10.1 - Exercises 39–52 concern simple interest.
52. Time...Ch. 10.1 - Future Value Compute the future value after 1 year...Ch. 10.1 - Future Value Compute the future value after 1 year...Ch. 10.1 - Effective Rate of Interest In Exercises 5558,...Ch. 10.1 - Effective Rate of Interest In Exercises 5558,...Ch. 10.1 - Effective Rate of Interest In Exercises 55–58,...Ch. 10.1 - Effective Rate of Interest In Exercises 55–58,...Ch. 10.1 - Prob. 59ECh. 10.1 - Savings Account During the 1990s, a deposit was...Ch. 10.1 - Prob. 61ECh. 10.1 - Prob. 62ECh. 10.1 - Prob. 63ECh. 10.1 - Doubling Time(True or False) An investment growing...Ch. 10.1 - Prob. 65ECh. 10.1 - Future Value If your stock portfolio gained 20% in...Ch. 10.1 - 67. Comparing Investments The same amount of money...Ch. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Prob. 70ECh. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - 76. Savings Account Ten thousand dollars is...Ch. 10.1 - Prob. 77ECh. 10.1 - Prob. 78ECh. 10.1 - Comparing Investments Consider the following two...Ch. 10.1 - 80. Comparing Investments Consider the following...Ch. 10.2 - Solutions can be found the section exercises....Ch. 10.2 - Prob. 2CYUCh. 10.2 - Prob. 3CYUCh. 10.2 - Exercises 1 and 2 describe increasing annuities....Ch. 10.2 - Exercises 1 and 2 describe increasing annuities....Ch. 10.2 - Exercises 3 and 4 describe decreasing annuities....Ch. 10.2 - Exercises 3 and 4 describe decreasing annuities....Ch. 10.2 - In Exercises 5 and 6, calculate the future value...Ch. 10.2 - In Exercises 5 and 6, calculate the future value...Ch. 10.2 - In Exercises 7 and 8, calculate the rent of the...Ch. 10.2 - In Exercises 7 and 8, calculate the rent of the...Ch. 10.2 - In Exercises 9 and 10, calculate the present value...Ch. 10.2 - In Exercises 9 and 10, calculate the present value...Ch. 10.2 - In Exercises 11 and 12, calculate the rent of the...Ch. 10.2 - In Exercises 11 and 12, calculate the rent of the...Ch. 10.2 - Savings Account Ethan deposits $500 into a savings...Ch. 10.2 - Savings Account Emma deposits $2000 into a savings...Ch. 10.2 - Prob. 15ECh. 10.2 - Savings Account A person deposits$5000 into a...Ch. 10.2 - In Exercises 17–20, determine the amount of...Ch. 10.2 - In Exercises 1720, determine the amount of...Ch. 10.2 - In Exercises 1720, determine the amount of...Ch. 10.2 - Prob. 20ECh. 10.2 - Comparing Payouts Is it more profitable to receive...Ch. 10.2 - Comparing Payouts Is it more profitable to receive...Ch. 10.2 - Comparing Bonus Plans When Bridget takes a new...Ch. 10.2 - Comparing Lottery Payouts A lottery winner is...Ch. 10.2 - College Allowance During Jacks first year at...Ch. 10.2 - Magazine Subscription Suppose that a magazine...Ch. 10.2 - 27. Savings Account Suppose that $1000 was...Ch. 10.2 - Savings Account Suppose that you opened a savings...Ch. 10.2 - 29. Savings Account Ms. Jones deposited $100 at...Ch. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Savings Account How much money must you deposit...Ch. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Municipal Bond A municipal bond pays 4% interest...Ch. 10.2 - Present Value What is the present value of a loan...Ch. 10.2 - 37. Business Loan A business loan for $200,000...Ch. 10.2 - 38. Lottery Payoff A lottery winner is to receive...Ch. 10.2 - Prob. 39ECh. 10.2 - A sinking fund is an increasing annuity set up by...Ch. 10.2 - Prob. 41ECh. 10.2 - A sinking fund is an increasing annuity set up by...Ch. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - A deferred annuity is a type of decreasing annuity...Ch. 10.2 - Prob. 50ECh. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Prob. 53ECh. 10.2 - Prob. 54ECh. 10.2 - Prob. 55ECh. 10.2 - Prob. 56ECh. 10.2 - Prob. 57ECh. 10.2 - In Exercises 51–58, give the settings or...Ch. 10.2 - Prob. 59ECh. 10.2 - 60. Time Interval A person deposits $800 at the...Ch. 10.2 - Prob. 61ECh. 10.2 - Home Repairs Fund Bob needs $3064 to have some...Ch. 10.2 - Prob. 63ECh. 10.3 - Solution can be found following the section...Ch. 10.3 - Solution can be found following the section...Ch. 10.3 - Solution can be found following the section...Ch. 10.3 - 1. Loan Payment A car loan of $10,000 is to be...Ch. 10.3 - Loan Payment A loan of $5000 is to be repaid with...Ch. 10.3 - Loan Payment A loan of $4000 is to be repaid with...Ch. 10.3 - Loan Payment A loan of $3000 is to be repaid with...Ch. 10.3 - Loan Amount The weekly payment on a 2-year loan at...Ch. 10.3 - Loan Amount The quarterly payment on a 5-year loan...Ch. 10.3 - Mortgage Payment Find the monthly payment on a...Ch. 10.3 - 8. Mortgage Payment Find the monthly payment on a...Ch. 10.3 - 9. Mortgage Amount Find the amount of a 30-year...Ch. 10.3 - Mortgage Amount Find the amount of a 25-year...Ch. 10.3 - Mortgage Balance A 30-year mortgage at 4.2%...Ch. 10.3 - 12. Mortgage Balance A 25-year mortgage at 4.5%...Ch. 10.3 - 13. Loan Interest A loan with a weekly payment of...Ch. 10.3 - Loan Interest A loan with a quarterly payment of...Ch. 10.3 - Amortization Schedule Write out a complete...Ch. 10.3 - Amortization Schedule Write out a complete...Ch. 10.3 - 17. Mortgage Consider a $204,700, 30-year mortgage...Ch. 10.3 - 18. Mortgage James buys a house for $370,000. He...Ch. 10.3 - 19. Car Loan Susie takes out a car loan for $9480...Ch. 10.3 - Loan Consider a $21,281.27 loan for 7 years at 8%...Ch. 10.3 - Prob. 21ECh. 10.3 - Comparing Financing Options In a recent year, Ford...Ch. 10.3 - 23. Comparing Financing Options A bank makes the...Ch. 10.3 - Buy Now or Later? According to an article in the...Ch. 10.3 - Balloon Payment A loan is to be amortized over an...Ch. 10.3 - 26. Balloon Payment A loan of $127,000.50 is to be...Ch. 10.3 - 27. Car Loan A car is purchased for $6287.10, with...Ch. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Terminating a Mortgage In 2006, Emma purchased a...Ch. 10.3 - Refinancing a Mortgage A real estate speculator...Ch. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Total of Loan Payment Suppose that you borrow...Ch. 10.3 - 36. Loan Amount Suppose that you borrow money at...Ch. 10.3 - Let Bn= balance of a loan after n payments, In=...Ch. 10.3 - Let QnandIn be as defined in Exercise 37. a. Use...Ch. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - In Exercises 39–46, give settings or statements to...Ch. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Debt Reduction A loan of $10,000 at 9% interest...Ch. 10.3 - 50. Debt Reduction A loan of $4000 at 6% interest...Ch. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.4 - Solution can be found following the section...Ch. 10.4 - Prob. 2CYUCh. 10.4 - Prob. 3CYUCh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Comparing IRAs Rework Examples 1 and 3 for the...Ch. 10.4 - Roth IRA Rework Exercise 5 for a Roth IRA.Ch. 10.4 - 8. Comparing IRAs Rework Examples 1 and 3 for the...Ch. 10.4 - Value of Starting an IRA Early Redo Example 4...Ch. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - 26. True or False Refer to Example 10. If the...Ch. 10.4 - Prob. 27ECh. 10.4 - APR In multiple-choice Exercises 2730, assume that...Ch. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Effective Mortgage Rate In multiple-choice...Ch. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Interest-Only Mortgage Consider a 15-year mortgage...Ch. 10.4 - 42. Interest-Only Mortgage Consider a 15-year...Ch. 10.4 - 43. Adjustable-Rate Mortgage Consider a 25-year...Ch. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.5 - Solution can be found following the section...Ch. 10.5 - Prob. 2CYUCh. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - In Exercises 1–10, give a difference equation for...Ch. 10.5 - In Exercises 1–10, give a difference equation for...Ch. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - In Exercises 11 and 12, answer the questions....Ch. 10.5 - In Exercises 11 and 12, answer the questions....Ch. 10.5 - Prob. 13ECh. 10.5 - In Exercises 1318, (a) determine the first five...Ch. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - In Exercises 1938, use difference equations to...Ch. 10.5 - In Exercises 1938, use difference equations to...Ch. 10.5 - In Exercises 19–38, use difference equations to...Ch. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Elevation and Atmospheric Pressure The atmospheric...Ch. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 50ECh. 10 - 1. What is meant by principal?
Ch. 10 - Prob. 2FCCECh. 10 - 3. What is meant by the balance in a savings...Ch. 10 - Prob. 4FCCECh. 10 - Prob. 5FCCECh. 10 - Prob. 6FCCECh. 10 - Prob. 7FCCECh. 10 - 8. Explain the difference between the nominal and...Ch. 10 - Prob. 9FCCECh. 10 - Prob. 10FCCECh. 10 - Prob. 11FCCECh. 10 - Prob. 12FCCECh. 10 - Prob. 13FCCECh. 10 - Prob. 14FCCECh. 10 - Prob. 15FCCECh. 10 - Prob. 16FCCECh. 10 - Prob. 17FCCECh. 10 - Prob. 18FCCECh. 10 - How are finance charges on a consumer loan...Ch. 10 - Prob. 20FCCECh. 10 - Prob. 21FCCECh. 10 - Prob. 22FCCECh. 10 - Prob. 23FCCECh. 10 - Prob. 24FCCECh. 10 - Prob. 25FCCECh. 10 - Prob. 26FCCECh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Nonstandard Mortgage A real estate investor takes...Ch. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Interest-Only Mortgage Consider a 25-year mortgage...Ch. 10 - 36. Adjustable-Rate Mortgage Consider a 25-year...Ch. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Suppose that a $100,000 investment grows 3% during...Ch. 10 - Prob. 2PCh. 10 - 3. Consider an annuity in which $100,000 is...Ch. 10 - Rework Exercise 3, where the interest rate is 4%...Ch. 10 - Prob. 5PCh. 10 - Prob. 6PCh. 10 - 7. Show that, if an investment of P dollars earns ...Ch. 10 - 8. Which of the following two statements is true?...Ch. 10 - Show that, if $1000 is invested at 8% interest...Ch. 10 - Prob. 10PCh. 10 - Prob. 11PCh. 10 - Prob. 12PCh. 10 - Prob. 13PCh. 10 - Prob. 14PCh. 10 - Prob. 15P
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