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Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Note Some of the formulas below use the special number e, which was presented in the Prologue.
Adjustable Rate Mortgage-Exact Payments This is a continuation of Exercise 30. In Exercise 30, we only approximated the increased payment when the rate for an ARM increases: We assumed that over the first 24 months, you accrue 0 equity in your home. (Your equity in a home is the total you have paid toward the principal.)We address that point here. We make use of the equity formula
E=P×(1+r)k−1(1+r)t−1.
Here E is the equity, in dollars, after k monthly payments. The quantities P, t, and r are defined as in Exercise 30. Round r to five decimal places.
We assume as in Exercise 30 that you borrowed $325,000 at an initial APR of 4.5% with a term of 30 years.
a. What equity have you accrued after 24 months?
b. When your rate adjusts to 7% after 24 months, the new amount borrowed is $325,000 less your equity. The term is now 28 years. What is your new monthly payment?
30. Adjustable Rate Mortgage-Approximating Payments An adjustable rate mortgage, or ARM, is a mortgage whose interest rate varies over the life of the loan. The interest rate is often tied in same fashion to the prime rate, which may go up or down. One advantage of an ARM is that it usually has an initial rate that is lower than that of a fixed rate mortgage. In the summer 2007, defaults on home mortgages led to a crisis in the U.S. economy. At least part of the blame was placed on ARMs. This exercise illustrates the difficulties that many homeowners faced during this period. We make use of the following formula for the monthly payment:
M=Pr(1+r)t(1+r)t−1.
Here M is the monthly payment, in dollars, P is the amount borrowed, in dollars, t is the term of the loan, in months, and r is the monthly interest rate as a decimal, with r=APR/12. In this exercise, round r to five decimal places.
Suppose you purchased a home in 2005, securing a mortgage of $325,000 with a 30-year ARM.
a. In 2005, interest rates were at a historical lows. Suppose that at the time of the loan, the rate for your ARM was a 4.5% APR. Calculate your monthly payment.
b. Suppose you earn $6000 per month. What percentage of your income is going toward your house payment?
c. Suppose that after 24 payments, your ARM rate adjusted to 7% APR. We will assume that after 24 months, your loan balance is still $325,000. (This is not as unreasonable an assumption as it may appear. The correct calculation is shown in Exercise 31.) What is your monthly payment now? Be careful: The term of the loan is now 28 years, not 30 years.
d. Using the assumptions of part c, what percentage of your income is going to your house payment now?
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Chapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Calculați (a-2023×b)²⁰²⁴arrow_forwardA student completed the problem below. Identify whether the student was correct or incorrect. Explain your reasoning. (identification 1 point; explanation 1 point) 4x 3x (x+7)(x+5)(x+7)(x-3) 4x (x-3) (x+7)(x+5) (x03) 3x (x+5) (x+7) (x-3)(x+5) 4x²-12x-3x²-15x (x+7) (x+5) (x-3) 2 × - 27x (x+7)(x+5) (x-3)arrow_forward2 Add the rational expressions below. Can you add them in this original form? Explain why or why not. 3x-7 5x + x² - 7x+12 4x-12 Show all steps. State your least common denominator and explain in words your process on how you determined your least common denominator. Be sure to state your claim, provide your evidence, and provide your reasoning before submitting.arrow_forward
- carol mailed a gift box to her sister the boxed gift weighed a total of 2 pounds the box alone weighed 13 ounces what was the wright of the giftarrow_forwardDirections: Use the table below to answer the following questions and show all work. Heights of Females 50.0 51.5 53.0 53.5 54.0 1. What is the average female height? 2. What are all the differences from the mean? 3. What is the variance for the female heights? 4. What is the standard deviation of the heights of the females? 5. What does the standard deviation found in number 4 represent? Write your answer in complete sentences.arrow_forward135 metr uzunlikdagi simni 6:3 nisbatda qismlarga am eatingarrow_forward
- MODELING REAL LIFE Your checking account has a constant balance of $500. Let the function $m$ represent the balance of your savings account after $t$ years. The table shows the total balance of the accounts over time. Year, $t$ Total balance 0 1 2 3 4 5 $2500 $2540 $2580.80 $2622.42 $2664.86 $2708.16 a. Write a function $B$ that represents the total balance after $t$ years. Round values to the nearest hundredth, if necessary. $B\left(t\right)=$ Question 2 b. Find $B\left(8\right)$ . About $ a Question 3 Interpret $B\left(8\right)$ . b represents the total balance checking and saving accounts after 8 years the balance would be 16 / 10000 Word Limit16 words written of 10000 allowed Question 4 c. Compare the savings account to the account, You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. A = 11998.70 SINCE 9000 is the principal ( 1+0.036/12)12 times 8 gives me aproxtimately 1997 14 / 10000 Word Limit14 words written of 10000 allowed Skip to…arrow_forwardListen MODELING REAL LIFE Your checking account has a constant balance of $500. Let the function m represent the balance of your savings account after t years. The table shows the total balance of the accounts over time. Year, t Total balance 0 $2500 1 $2540 2 $2580.80 3 $2622.42 4 $2664.86 5 $2708.16 a. Write a function B that represents the total balance after t years. Round values to the nearest hundredth, if necessary. B(t) = 500 + 2000(1.02)* b. Find B(8). About $2843.32 Interpret B(8). B I U E T² T₂ c. Compare the savings account to the account, You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. B I U E E T² T₂ A = 11998.70 SINCE 9000 is the principal (1+0.036/12)12 times 8 gives me aproxtimately 1997arrow_forwardWhat are the answers for star powerarrow_forward
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