chapter 4 math 1010

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Decide whether the statement makes sense. Explain your reasoning.

1. My annual income after tax is only $25,000. I need to cut back on my non essential spending. Something has to go either the mango smoothies, the movies, or the vacation. I figure it’s the vacation that is i making the biggest dent in my budget. I take a vacation once a year which costs about $1100. I go to the movies once a week and spend a total of $17 and I have a mango smoothie every day at my favorite cafe. It costs $4.50 plus tax.

2. Steve is planning to open a saving account either at Quarterly

3. I have a fixed-rate 30-year mortgage of 120,000 at 7%. I inherited some money recently. If I pay off my mortgage in 20 years instead of 30, the total amount of interest I will end up paying will be less.

4. I have a 30-year mortgage and have been paying it off for 5 years now so I should have paid off about one sixth of the principal by now.

5. I make only the minimum required payments on my credit card balance each month, because that way I’ll save money in the long run.

6. If interest rates stay at 4% APR and continue to make my monthly $25 deposits into my retirement plan, I should be able to retire in 30 years with comfortable income.

Part II: BASIC SKILLS AND CONCEPTS. Write out all formulas used.

The expenses and income of an individual are given in table form. FInd the net monthly cash flow (it could be positive or negative). Assume salaries and wages are after taxes, that 1 month=4 weeks, and that 1 year= 12 months. Round your answer to the nearest dollar.

7)

Income

Expenses

Part-time job: $800/ month

Student loan: $7500/year

Scholarship: $4600/year

Rent: $540/month

Groceries: $65/week

Tuition and fees: $3200 twice a year

Entertainment: $160/month

Use the information below to answer questions 8 and 9

You currently drive 360 miles per week in a car that gets 20 miles per gallon of gas. You are considering buying a new fuel-efficient car for 12,000 (after trade-in on your current car) that gets 60 miles per gallon. Insurance premiums for the new and old car are $900 and $600 per year, respectively. You anticipate spending $1400 per year on repairs for the old car and having no repairs on the new car. Assume gas costs 3.50 per gallon.

8) Over a five-year period, how much does it cost to operate and maintain your old car.

9) Over a five year period, how much would it cost to purchase, operate, and maintain the new car you are considering buying? Is it less expensive to keep the old car or buy the new

Car?

Find the monthly interest payments in the situation described. Assume that the monthly interest rates are 1/12 of annual interest rates.

10) Ashton maintains an average balance of $1000 on his credit card which carries an annual interest rate of 15%

Use the given principal, interest rate, and time period to answer questions 11 and 12

Principal: $9500 Rate:4.6% Years: 3

11) Determine the amount of interest that would be earned in an account paying simple interest.

12) Determine the amount of interest that would be earned in an account, With interest compounded annually. How much more interest would be earned in the compound interest account compared to the simple interest account?

Solve the problem.

13) Suppose you start saving today for a $30,000 down payment that you plan to make on a house in 15 years. Assume that you make no deposits into the account after your initial deposits. The account has monthly compounding and APR of 4%. How much would you need to deposit now to reach your $30,000 goal in 15 years.

14) You put $334 per month in an investment plan that pays an APR of 4%. How much money will you have after 25 years.

15) For the investment plan in question 14, what is the total amount that you deposited to the account over the time period? How much did you earn in interest?

For the loan described, calculate the portions of the payments that go to principal and to interest during the first 2 months, and the new balance after each payment. Show all work and fill in the table.

16) Make an amortization tale showing the portions of the payments that go to the principal and to interest, and the new balance after each payment, during the first 2 months for a home mortgage of $106,974 with a fixed APR of 7.0% for 20 years. Hint: Find the monthly payment first.

Payment Number

Interest

Principal

Balance

0

106,974

1

2

Part III: Further Applications. You must show . Write all formulas and values used.

17) Suppose you have the following three student loans.:

$10,000 with an APR of 6.5% for 15 years

$15,000 with an APR of 7% for 20 years

$12,500 with an APR of 7.5% for 10 years

  1. Calculate the monthly payment for each loan individually

b. Calculate the total you’ll pay in payments during the life of all three loans combined.

c. A bank offers to consolidate your three loans into a single loan with an APR of 6.5% and a loan term of 15 years. What will your monthly payments be in that case? What will your total [payments be over the 15 years.

d. Discuss the pros and cons of accepting this loan consolidation

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