Chapter 20 Practice Problems

  1. I put $2,000 in the bank, and two years later after being compounded monthly, it had grown to $4,000.
    1. What was the effective annual yield?
    2. What was the APR?
    3. What would have been the effective annual yield if the compounding had been continuous instead of monthly?

  2. I make a regular deposit monthly into an account bearing 5% APR, compounded monthly.
    1. If my deposit is $150, and I do this for four years, how much will I have in my account?
    2. What would my monthly deposit need to be to get this same amount in 3 years?

  3. I want to buy a car.
    1. The car I really want costs $35,000. If I can afford $450/month, and the present interest rate is 8.9%, will I be able to get the car on a 4-year loan?
    2. How long would the loan have to go so that I could afford this car with $1000 monthly payments?
    3. What would the interest rate have to be so that a $800/month payment would pay off the loan in 5 years?

  4. I have a well out back. I'm told that at my present usage, I'll have enough water to last 100 years.
    1. What is my static reserve?
    2. If every year I use 10% more water, what is my exponential reserve?
    3. By what percentage could I raise my water usage annually so that the water in the well would last exactly 50 years?

  5. A certain population of bacteria has the following reproduction curve, with the populations being measured in millions:
    1. What are the equilibrium population sizes?
    2. What would the population have to be so that the sustainable yield would be 10,000,000?
    3. For which population would there be a maximum sustainable yield?
    4. If the population this year was 10,000,000, complete the table below:
      Year, starting with this one Population
      0 .
      1 .
      2 .
      3 .
      4 .