Midterm Practice Problems

1. Your car gets 30 miles to the gallon on highway trips. You have $50 and gas costs on average $1.40 per gallon. How far can you afford to drive?
2. In 1990 the cost of a certain computer was $1500, 30% less than the cost in 1980. What was the price of the computer in 1980?
3. If the number of highway accidents increased 10% last year and decreased 8% this year, what was the overall percentage increase or decrease in the number of highway accidents?
4. Greg Ostertag is 17.8% taller than John Stockton. What percent shorter is John Stockton?
5. If an afternoon movie costs $3.50 and a night movie costs $6.00. How much cheaper is the afternoon movie? How much more expensive is the night movie? (express your answers both in absolute terms and as percentages)
6. Planet Xenon is about $2.5 \times 10^{4}$ figors from planet Argon. If we consider a scale factor of 3.4 billion, what is the scaled distance in miles between Xenon and Argon? Be sure to consider the relevant precision or significant digits.(1 figor = 3.6 million km)
7. Convert 60 pounds per square inch to grams per square centimeter.
8. Suppose that in 1980 the average rent for a two bedroom apartment was $250, whereas today it would be $600. Which of the following statements are true? If they are false correct the percentage. All answers must be justified by a computation.
   1. The average rental cost increased 140% from 1980 to 1999.
   2. The average rental cost today is 140% of what is was in 1980.
   3. The average rental cost in 1980 is 58.3% of what it is today.
   4. The average rental cost was 58.3% lower in 1980 than today's cost.
9. You are considering opening a savings account. Bank A is offering a 3.7% APR with monthly compounding and bank B is offering 3.6% APR with daily compounding. Which bank should you choose? Justify your answer.
10. You want to save $50,000 over the next 18 years. Assume an APR of 8% with monthly compounding. How much would you have to deposit today (and leave alone) to reach your savings goal? How much would you have to deposit each month to reach your savings goal?
11. If a bank account is continuously compounding interest at an 6.5% APR, how much money would you have after 12 years if you deposited $3400 initially? What is you annual percentage yield (APY) for this account?
12. You open a savings account with a 4% APR by depositing $100 per month for two years. Then, you get a raise and you increase your monthly payments to $150 per month. You continue to save for 3 more years. How much money do you have in your account after your 5 years of savings?
13. You are saving for retirement. When you retire you want to live off only the interest from your savings. You want to have $40,000 per year to live on. Suppose you will be saving for 40 years. Assume an APR of 8%. How much do you have to save per month to reach your goal? (To make your calculation easier assume simple interest after retirement.)
14. You buy a $135,000 house. You take a mortgage with an APR of 7% for 30 years.
    1. What will your monthly payment be?
    2. As a percentage of the total amount you pay back, how much interest did you pay?
15. You can afford $250 per month for car payments, and you are able to get a loan for 5 years with an APR of 7%.
    1. With no down payment, what is the most expensive car you can afford?
    2. If you had some savings to cover a down payment of 9% of the car price, what is the most expensive car you can afford?

**You will be given the savings plan formula and loan payment formula.