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Study Guides > Mathematics for the Liberal Arts

Exercises

Skills

  1. A friend lends you $200 for a week, which you agree to repay with 5% one-time interest. How much will you have to repay?
  2. Suppose you obtain a $3,000 T-note with a 3% annual rate, paid quarterly, with maturity in 5 years. How much interest will you earn?
  3. A T-bill is a type of bond that is sold at a discount over the face value. For example, suppose you buy a 13-week T-bill with a face value of $10,000 for $9,800. This means that in 13 weeks, the government will give you the face value, earning you $200. What annual interest rate have you earned?
  4. Suppose you are looking to buy a $5000 face value 26-week T-bill. If you want to earn at least 1% annual interest, what is the most you should pay for the T-bill?
  5. You deposit $300 in an account earning 5% interest compounded annually. How much will you have in the account in 10 years?
  6. How much will $1000 deposited in an account earning 7% interest compounded annually be worth in 20 years?
  7. You deposit $2000 in an account earning 3% interest compounded monthly.
    1. How much will you have in the account in 20 years?
    2. How much interest will you earn?
  8. You deposit $10,000 in an account earning 4% interest compounded monthly.
    1. How much will you have in the account in 25 years?
    2. How much interest will you earn?
  9. How much would you need to deposit in an account now in order to have $6,000 in the account in 8 years? Assume the account earns 6% interest compounded monthly.
  10. How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.
  11. You deposit $200 each month into an account earning 3% interest compounded monthly.
    1. How much will you have in the account in 30 years?
    2. How much total money will you put into the account?
    3. How much total interest will you earn?
  12. You deposit $1000 each year into an account earning 8% compounded annually.
    1. How much will you have in the account in 10 years?
    2. How much total money will you put into the account?
    3. How much total interest will you earn?
  13. Jose has determined he needs to have $800,000 for retirement in 30 years.   His account earns 6% interest.
    1. How much would you need to deposit in the account each month?
    2. How much total money will you put into the account?
    3. How much total interest will you earn?
  14. You wish to have $3000 in 2 years to buy a fancy new stereo system. How much should you deposit each quarter into an account paying 8% compounded quarterly?
  15. You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest.
    1. How much do you need in your account at the beginning
    2. How much total money will you pull out of the account?
    3. How much of that money is interest?
  16. How much money will I need to have at retirement so I can withdraw $60,000 a year for 20 years from an account earning 8% compounded annually?
    1. How much do you need in your account at the beginning
    2. How much total money will you pull out of the account?
    3. How much of that money is interest?
  17. You have $500,000 saved for retirement. Your account earns 6% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?
  18. Loren already knows that he will have $500,000 when he retires. If he sets up a payout annuity for 30 years in an account paying 10% interest, how much could the annuity provide each month?
  19. You can afford a $700 per month mortgage payment. You’ve found a 30 year loan at 5% interest.
    1. How big of a loan can you afford?
    2. How much total money will you pay the loan company?
    3. How much of that money is interest?
  20. Marie can afford a $250 per month car payment. She’s found a 5 year loan at 7% interest.
    1. How expensive of a car can she afford?
    2. How much total money will she pay the loan company?
    3. How much of that money is interest?
  21. You want to buy a $25,000 car. The company is offering a 2% interest rate for 48 months (4 years). What will your monthly payments be?
  22. You decide finance a $12,000 car at 3% compounded monthly for 4 years. What will your monthly payments be? How much interest will you pay over the life of the loan?
  23. You want to buy a $200,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest.
    1. How much is the loan amount going to be?
    2. What will your monthly payments be if the interest rate is 5%?
    3. What will your monthly payments be if the interest rate is 6%?
  24. Lynn bought a $300,000 house, paying 10% down, and financing the rest at 6% interest for 30 years.
    1. Find her monthly payments.
    2. How much interest will she pay over the life of the loan?
  25. Emile bought a car for $24,000 three years ago. The loan had a 5 year term at 3% interest rate. How much does he still owe on the car?
  26. A friend bought a house 15 years ago, taking out a $120,000 mortgage at 6% for 30 years. How much does she still owe on the mortgage?
  27. Pat deposits $6,000 into an account earning 4% compounded monthly. How long will it take the account to grow to $10,000?
  28. Kay is saving $200 a month into an account earning 5% interest. How long will it take her to save $20,000?
  29. James has $3,000 in credit card debt, which charges 14% interest. How long will it take to pay off the card if he makes the minimum payment of $60 a month?
  30. Chris has saved $200,000 for retirement, and it is in an account earning 6% interest. If she withdraws $3,000 a month, how long will the money last?

Concepts

  1. Suppose you invest $50 a month for 5 years into an account earning 8% compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 25 years. How much will you have in the end?
  2. Suppose you put off making investments for the first 5 years, and instead made deposits of $50 a month for 25 years into an account earning 8% compounded monthly. How much will you have in the end?
  3. Mike plans to make contributions to his retirement account for 15 years. After the last contribution, he will start withdrawing $10,000 a quarter for 10 years. Assuming Mike's account earns 8% compounded quarterly, how large must his quarterly contributions be during the first 15 years, in order to accomplish his goal?
  4. Kendra wants to be able to make withdrawals of $60,000 a year for 30 years after retiring in 35 years. How much will she have to save each year up until retirement if her account earns 7% interest?
  5. You have $2,000 to invest, and want it to grow to $3,000 in two years. What interest rate would you need to find to make this possible?
  6. You have $5,000 to invest, and want it to grow to $20,000 in ten years. What interest rate would you need to find to make this possible?
  7. You plan to save $600 a month for the next 30 years for retirement. What interest rate would you need to have $1,000,000 at retirement?
  8. You really want to buy a used car for $11,000, but can only afford $200 a month. What interest rate would you need to find to be able to afford the car, assuming the loan is for 60 months?

Exploration

  1. Pay day loans are short term loans that you take out against future paychecks: The company advances you money against a future paycheck. Either visit a pay day loan company, or look one up online. Be forewarned that many companies do not make their fees obvious, so you might need to do some digging or look at several companies.
    1. Explain the general method by which the loan works.
    2. We will assume that we need to borrow $500 and that we will pay back the loan in 14 days. Determine the total amount that you would need to pay back and the effective loan rate. The effective loan rate is the percentage of the original loan amount that you pay back. It is not the same as the APR (annual rate) that is probably published.
    3. If you cannot pay back the loan after 14 days, you will need to get an extension for another 14 days. Determine the fees for an extension, determine the total amount you will be paying for the now 28 day loan, and compute the effective loan rate.
  2. Suppose that 10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
    1. Let's consider your existing mortgage:
      1. How much money did you pay as your down payment?
      2. How much money was your mortgage (loan) for?
      3. What is your current monthly payment?
      4. How much total interest will you pay over the life of the loan?
    2. This year, you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.
      1. How much of the loan have you paid off? (i.e., how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)
      2. How much money have you paid to the loan company so far?
      3. How much interest have you paid so far?
      4. How much equity do you have in your home (equity is value minus remaining debt)
    3. Since interest rates have dropped, you consider refinancing your mortgage at a lower 6% rate.
      1. If you took out a new 30 year mortgage at 6% for your remaining loan balance, what would your new monthly payments be?
      2. How much interest will you pay over the life of the new loan?
    4. Notice that if you refinance, you are going to be making payments on your home for another 30 years. In addition to the 10 years you've already been paying, that's 40 years total.
      1. How much will you save each month because of the lower monthly payment?
      2. How much total interest will you be paying (you need to consider the amount from 2c and 3b)
      3. Does it make sense to refinance? (there isn't a correct answer to this question. Just give your opinion and your reason)

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