Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN: 9781337111348
Author: Bruce Crauder, Benny Evans, Alan Noell
Publisher: Cengage Learning
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Chapter P, Problem 16E
The Truth in Lending Act Many lending agencies compound interest more often than yearly, and, as we noted in Example P.2, they are required to report the annual percentage rate, or APR, in a prominent place on the loan agreement. Furthermore, they are required to calculate the APR in a specific way. If
a. Suppose a credit card company charges a monthly interest rate of
b. The phrase annual percentage rate leads some people to believe that if you barrow
c. If Interest is calculated monthly (which is common), then the actual amount you would owe in the situation of part b is given by
What is the actual amount you would owe at the end of a year?
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Chapter P Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Ch. P - Calculate the following expression and round to...Ch. P - If the annual percentage rate is 8% and the...Ch. P - Valentines Day According to the National Retail...Ch. P - Pet Owners According to the Humane Society, in...Ch. P - A Billion Dollars A one dollar bill is 0.0043 inch...Ch. P - National Debt In mid-2015 the U.S. population was...Ch. P - 10% Discount and 10% Tax Suppose you want to buy a...Ch. P - A Good Investment You have just received word that...Ch. P - A Bad Investment You have just received word that...Ch. P - An Uncertain Investment Suppose you invested 1300...
Ch. P - Pay Raise You receive a raise in your hourly pay...Ch. P - Heart Disease In a certain country, the number of...Ch. P - Trade Discount Often retailers sell merchandise at...Ch. P - Series Discount This is a continuation of Exercise...Ch. P - Present Value Present value is the amount of money...Ch. P - Future Value Business and finance texts refer to...Ch. P - The Rule of 72 This is a continuation of Exercise...Ch. P - The Truth in Lending Act Many lending agencies...Ch. P - The Size of the Earth The radius of the Earth is...Ch. P - When the Radius Increases a. A rope is wrapped...Ch. P - The Length of Earths Orbit The Earth is...Ch. P - Prob. 20ECh. P - Prob. 21ECh. P - Prob. 22ECh. P - Prob. 23ECh. P - Lean Body Weight in Males A persons lean body...Ch. P - Lean Body Weight in Females This is a continuation...Ch. P - Mannings Equation Hydrologists sometimes use...Ch. P - Relativistic Length A rocket ship travelling near...Ch. P - Equity in a Home When you purchase a home by...Ch. P - The Advantage Cash Card At the student union on a...Ch. P - Prob. 1SBECh. P - Prob. 2SBECh. P - Prob. 3SBECh. P - Basic Calculations 7.61.79.2Ch. P - Parenthesis and Grouping 7.3-6.82.5+1.8Ch. P - Prob. 6SBECh. P - Parentheses and Grouping 6+e+13Ch. P - Parentheses and Grouping -e+eCh. P - Prob. 9SBECh. P - Prob. 10SBECh. P - Prob. 11SBECh. P - Prob. 12SBECh. P - Prob. 13SBECh. P - Prob. 14SBECh. P - Prob. 15SBECh. P - Prob. 16SBECh. P - Arithmetic In Exercises S-16 through S-20, perform...Ch. P - Prob. 18SBECh. P - Prob. 19SBECh. P - Prob. 20SBECh. P - Prob. 21SBECh. P - Prob. 22SBECh. P - Prob. 23SBECh. P - Prob. 24SBECh. P - Prob. 25SBECh. P - Prob. 26SBECh. P - Prob. 27SBECh. P - Prob. 28SBECh. P - Prob. 29SBECh. P - Evaluating Formulas In Exercises S-21 through...Ch. P - Lending Money For a certain loan, the interest I...Ch. P - Monthly Payment For a certain instalment loan, the...Ch. P - Prob. 33SBECh. P - A Skydiver When a skydiver jumps from an airplane,...Ch. P - Future Value In certain savings scenarios, the...Ch. P - A Population of Deer The number N of deer in a...Ch. P - Prob. 37SBECh. P - Getting Three Sixes If we roll n fair dice, then...Ch. P - Prob. 1CRCh. P - Prob. 2CRCh. P - Prob. 3CRCh. P - Prob. 4CRCh. P - Keplers Third Law According to Keplers third law...Ch. P - Traffic Signal Traffic engineers study how long...
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- APR and EAR Recall that the APR the annual percentage rate is the percentage rate on a loan that the Truth in Lending Act requires lending institutions to report on loan agreements. It does not tell directly what the interest rate really is. If you borrow money for 1 year and make no payments, then in order to calculate how much you owe at the end of the year, you must use another interest rate, the EAR the effective annual rate, which is not normally reported on loan agreements. The calculation is made by adding the interest indicated by the EAR to the amount borrowed. The relationship between the APR and the EAR depends on how often interest is compounded. If you borrow money at an annual percentage rate APR as a decimal, and if interest is compounded n times per year, then the effective annual rate EAR as a decimal is given by EAR=(1+APRn)n1. For the remainder of this problem, we will assume an APR of 10 thus, in the formula above, we would use 0.1 in place of APR. a. Would you expect a larger or a smaller EAR if interest is compounded more often? Explain your reasoning. b. Make a table that shows how the EAR depends on the number of compounding periods. Use your table to report the EAR if interest is compounded once each year, monthly, and daily. note: The formula will given the EAR as a decimal. You should report your answer as a percent with three decimal places. c. If you borrow 5000 and make no payments for 1 year, how much will you owe at the end of a year if interest is compounded monthly? If interest is compounded daily? d. If interest is compounded as often as possiblethat is, continuouslythen the relationship between APR and EAR is given by EAR=eAPR1. Again using an APR of 10, compare the EAR when the interest is compounded monthly with the EAR when the interest is compounded continuously.arrow_forwardContinued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.arrow_forwardHome Equity When you purchase a home by securing a mortgage, the total paid toward the principle is your equity in the home. If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E in dollars, after k monthly payments is given by E=P(1+r)k1(1+r)t1 Here r is the monthly interest rate as a decimal, with r=APR/12 Suppose you have a mortgage of 425,000 at an APR of 9% and a term of 30 years. How long does it take for your equity to reach half of the amount of the original mortgage? Round r to four decimal places.arrow_forward
- Equity in a Home When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. Technically, the lending agency calculates your equity by subtracting the amount you still owe on your mortgage from the current value of your home, which may be higher or lower than your principal. Assume that your mortgage is for 350, 000 at a monthly rate of 0.007 as a decimal and that the term of the mortgage is 30 years. Then your equity after k monthly payments is 350, 0001.007k-11.007360-1 dollars. Calculate the equity in your home after 10 years.arrow_forwardAn Uncertain Investment Suppose you invested 1300 in the stock market two years ago. During the first year the value of the stock increased by 12%. During the second year, the value of the stock decreased by 12%. How much money is your investment worth at the end of the two-year period? Did you earn money or lose money? Note: The answer to the first question is not 1300arrow_forwardEquity: When you use a mortgage to purchase a home, the leading institution effectively owns the home. You buy back part ownership in the home with each monthly payment. The part you have bought back is your equity in the home. If the mortgage amount is P dollars, the monthly interest rate is r as a decimal, and the term of the mortgage is t months, then your equity after k payments is E(k)=P((1+r)k1)(1+r)t1dollars In this exercise, assume that the mortgage amount is 200,000, the APR is 6so r=0.06/12, and the term of the loan is 30 years 360 months. a. Find a formula for the equity. b. Make a graph of the equity over 360 months, the term of the loan. c. Does the graph show that you have half-ownership in the home halfway through the term of the mortgage?arrow_forward
- Your Childs Education You want to begin making regular deposits to finance your childs college education 18 years 216 months in the future. You are able to invest 200 at the end of each month, and you judge that 100, 000 will be needed. That is, you want the future value F of the investment to be 100, 000. Whether you can attain that goal depends on interest rates. If the monthaly interest rate is r as a decimal, then the future value of the investment is given by F=200r1+r216-1 dollars. a. Plot the graph of F along with the target value of 100, 000. Use a horizontal span of 0 to 0.01. b. Fina the monthly rate r that will yield the dsired future value of 100, 000. Round your answer as a percentage to one decimal place. c. What is your total investment in your childs education?arrow_forwardAn Amortization Table Suppose you borrow P dollars at a monthly interest rate of r as a decimal and wish to pay off the loan in t months. Then your monthly payment can be calculated using M=Pr(1+r)t(1+r)t1 dollars. Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow 3500 at a 9 APR meaning that you use r = 0.09/12 in the preceding formula and pay it back in 2 years. a. What is your monthly payment? b. Lets look ahead to the time when the loan is paid off. i. What is the total amount you paid to the bank? ii. How much of that was interest? c. The amount B that you still owe the bank after making k monthly payments can be calculated using the variables r, P, and t. The relationship is given by B=P((1+r)t(1+r)k(1+r)t1) dollars. i. How much do you still owe the bank after 1 year of payments? ii. An amortization table is a table that shows how much you still owe the bank after each payment. Make an amortization table for this loan.arrow_forward
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