Concept explainers
Home 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
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Suppose you have a mortgage of
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Lending Money For a certain loan, the interest I due at the end of a loan period is given by I=Prt, where P is the principal barrowed, r is the yearly interest rate as a decimal, and t is the number of years since the money was barrowed. What interest is accrued if 3 years ago we barrowed 5000 at an interest rate of 5%?arrow_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_forwardFuture Value In certain savings scenarios, the value F of an investment after t years, the future value, is given by F=P1+rt. Here r is the yearly interest rate as a decimal, P is the amount of the original investment and t is the term of the investment. If we invest 1000 at an interest rate of 0.06 per year as a decimal, and if the term of the investment is 5 years, what is the future value?continuedarrow_forward
- SalaryA Colleague of the teacher in Exercise 29, hired at the same time, makes $35,000 in her first year and gets a $1200 raise each year. (a) What is her salary Anin her nth year at this school? (b) Find her salary in her eighth year at this school, and compare it to the salary of the teacher in Exercise 29 in his eighth year.arrow_forwardCar Rental A businessman intends to rent a car for a 3-day business trip. The rental is 65 a day and 15 per mile Plan 1 or 90 a day with unlimited mileage Plan 2. He is not sure how many miles he will drive but estimates that it will be between 400 and 800 mi. a For each plan, find a formula for the cost C in terms of the number x of miles driven. b Which rental plan is cheaper if the businessman drives 400 miles? 800 miles? c At what mileage do the two plans cost the same?arrow_forwardPaying Off a Credit Card Suppose you owe 15, 000 on a credit card that carries an APR of 24. Because the balance is so high, you choose to stop charging and pay off the card. You can afford to make only the minimum monthly payment, which is 5 of the balance. Then your balance after t months is given by B=15,000(1.020.95)tdollars. How many payments will you have to make to get the balance below 100?arrow_forward
- Investments Jack invest $1000 at a certain annual interest rate, and he invests another $2000 at an annual rate that is one half percent higher. If he receives a total of $190 interest in 1 year, at what rate is the $1000 invested?arrow_forwardProfit = revenue cost Cost and Revenue A tire company determines that to manufacture a certain type of tire, it costs $8000 to set up the production process. Each tire that is produced costs $22 in material and labor. The company sells this tire to wholesale distributors for $49 each. (a) Find a formula for the cost C of producing x tires? (b) Find a formula for the revenue R from selling x ? (c) Find a formula for the profit P from selling x tires? (d)How many tires must the company sell to break even?arrow_forwardDrug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?arrow_forward
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