Monthly Payment For a certain instalment loan, the monthly payment
where
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- 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 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_forwardBorrowing Money You borrow $5000 from your parents to purchase a used car. The arrangements of the loan are such that you make payments of $250 per month toward the balance plus 1 interest on the unpaid balance from the previous month. (a) Find the first year’s monthly payments and the unpaid balance after each month. (b) Find the total amount of interest paid over the term of the loan.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_forward
- Paying 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_forwardSalaryA 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_forwardDistance and Time Anthony leaves Kingstown at 2:00 P.M. and drives to Queensville, 160 mi distant, at 45 mi/h. at 2:15 P.M. Helen leaves Queensville and drives to Kingstown at 40 mi/h. At what time do they pass each other on the road?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_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_forward
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