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6.3–6.4 Quiz

6.3–6.4 Quiz
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  • 1. Buying a House

    You want to buy a $100,000 house. You plan to make a $20,000 down payment.

    Each month for 5 years, you deposit $300 into a savings account that earns 5%, compounded monthly. After 5 years, you use the money in the account to make the down payment.

    1. How much is left in the account?
    2. You leave the remaining amount from part (a) in the account. Assuming you do not make any more deposits, how much is in the account after 14 years?
    • Worked-Out Solution

      a. Use the formula for the balance in an increasing annuity.

      So, after making the down payment of $20,000, you have

      left in your account.

      b. Use the formula for compound interest, compounded monthly.

      So, at the end of 14 years, you will have a little more than $800 in your account.

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  • 2. Comparing Interest

    You want to buy a $100,000 house. You plan to make a $20,000 down payment.

    You take out a home mortgage for $80,000 for 30 years. Compare the total interest you pay for the annual percentage rates.

    a. 5%

    b.7%

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      _  _     ______   _____       ___      _____   
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     `-` -`   `-----`   -----`   `-`   `-`   `---`   
                                                     
    
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  • 3. Making Extra Payments

    You take out a home mortgage for $80,000 for 30 years at 5.5%. Each month, you make the regular payment of $454.23 plus an additional $50.

    1. How much sooner do you pay off the mortgage?
    2. How much do you save in interest?
    • Worked-Out Solution

      Use a spreadsheet.

      1. You pay the mortgage off months (over 6 years) sooner.
      2. If you had paid monthly payments for 360 months, you would have paid

        in interest. By making the additional payments each month, you saved

        in interest. This is enough money to buy a nice car!

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     `-----`    `---`    `-` --`   `---`    |_|`-`   
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  • 4. Buying Versus Renting

    You want to buy a $100,000 house. You plan to make a $20,000 down payment. You take out a home mortgage for $80,000 for 30 years at 6%. After 5 years, you move to a different state and sell the home for $140,250.

    Compare the costs of buying the home and renting a comparable home for $550 per month. Assume that if you did not buy the home, you could have invested the down payment and earned $4000 in interest.

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    | '--' ||   -| ||-  | |/\| || | || | || |  --  // 
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    |_|| |_||  /_____// |_// \_||  \____//  |______// 
    `-`  `-`   `-----`  `-`   `-`   `---`   `------`  
                                                      
    
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  • 5. Retirement Plan

    You start your working career when you are 22 years old. Each month, you deposit $150 into a retirement plan that earns 6%, compounded monthly. You continue making deposits into the plan until you are 67 years old.

    Find the balance in the account.

    • Worked-Out Solution

      Use the formula for the balance in an increasing annuity.

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      ______   _    _     _____      ___      ____    
     /_   _// | || | ||  / ____||   / _ \\   |  _ \\  
       | ||   | || | || / //---`'  | / \ ||  | |_| || 
      _| ||   | \\_/ || \ \\___    | \_/ ||  | .  //  
     /__//     \____//   \_____||   \___//   |_|\_\\  
     `--`       `---`     `----`    `---`    `-` --`  
                                                      
    
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  • 6. Retirement Plan

    You start your working career when you are 22 years old. Each month, you deposit $150 into a retirement plan that earns 6%, compounded monthly. You continue making deposits into the plan until you are 67 years old.

    How many years can the account support withdrawals of $70,000 a year?

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    | |__/ || | \\_/ || | .  . ||    | ||    | .  //  
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     -----`     `---`   `-`  `-`     `-`'    `-` --`  
                                                      
    
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