Ron Larson
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6.4 Savings & Retirement Plans

6.4 Savings & Retirement Plans
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  • 1. Savings Account

    You deposit $1000 into a savings account. The savings account earns 5%, compounded monthly. Find the balance in the account after each time period. (See Example 1.)

    1. 10 years
    2. 20 years
    • Worked-Out Solution

      Use the formula for compound interest.

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      ______     ___      _  _    _    _      _____  
 /_   _//   / _ \\   | \| || | || | ||   / ___// 
 `-| |,-   | / \ ||  |  ' || | || | ||   \___ \\ 
   | ||    | \_/ ||  | .  || | \\_/ ||   /    // 
   |_||     \___//   |_|\_||  \____//   /____//  
   `-`'     `---`    `-` -`    `---`   `-----`
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  • 2. Savings Account

    Suppose that you deposit $1000 into a savings account. The savings account earns 6%, compounded monthly. Find the balance in the account after each time period. (See Example 1.)

    1. 10 years
    2. 20 years
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      ______    ______  __    __    _____    _    _   
 /_   _//  /_   _// \ \\ / //  |  ___|| | || | || 
 `-| |,-    -| ||-   \ \/ //   | ||__   | || | || 
   | ||     _| ||_    \  //    | ||__   | \\_/ || 
   |_||    /_____//    \//     |_____||  \____//  
   `-`'    `-----`      `      `-----`    `---`
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  • 3. Savings Account

    You deposit $1000 into a savings account. The savings account earns 5.5%, compounded monthly. Your friend deposits $700 into a savings account that earns 7.5%, compounded monthly. Which account has the greater balance after 15 years? (See Example 1.)

    • Worked-Out Solution

      Use the formula for compound interest.

      Your Account:

      Your Friend's Account:

      Your account has a greater balance after 15 years.

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       _____   __   __    _  __   __   __   ______   
  / ___//  \ \\/ //  | |/ //  \ \\/ // |      \\ 
  \___ \\   \ ` //   | ' //    \ ` //  |  --  // 
  /    //    | ||    | . \\     | ||   |  --  \\ 
 /____//     |_||    |_|\_\\    |_||   |______// 
`-----`      `-`'    `-` --`    `-`'   `------`
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  • 4. Savings Account

    Suppose that you deposit $1000 into a savings account. The savings account earns 6.5%, compounded monthly. Your friend deposits $600 into a savings account that earns 8%, compounded monthly. Which account has the greater balance after 40 years? (See Example 1.)

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      ____       ___     _____       ___      _  __  
 |  _ \\    / _ \\  |  __ \\    / _ \\   | |/ // 
 | |_| ||  | / \ || | |  \ ||  | / \ ||  | ' //  
 | .  //   | \_/ || | |__/ ||  | \_/ ||  | . \\  
 |_|\_\\    \___//  |_____//    \___//   |_|\_\\ 
 `-` --`    `---`    -----`     `---`    `-` --`
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  • 5. Purchase of Manhattan

    According to legend, in 1626, Peter Minuit purchased Manhattan Island from Native Americans for $24 worth of trade goods. Suppose the $24 had been deposited into a savings account earning 7%, compounded annually. How much would be in the account in 2014? (See Example 2.)

    • Worked-Out Solution

      From 1626 to 2014 is 388 years. Use the formula for compound interest.

      So, about $6 trillion would be in the account in 2014.

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     _    _      ___      ____     __   __   _____    
| |  | ||   / _ \\   |  _ \\   \ \\/ // |  __ \\  
| |/\| ||  | / \ ||  | |_| ||   \ ` //  | |  \ || 
|  /\  ||  | \_/ ||  | .  //     | ||   | |__/ || 
|_// \_||   \___//   |_|\_\\     |_||   |_____//  
`-`   `-`   `---`    `-` --`     `-`'    -----`
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  • 6. Gift for the Future

    You deposit $3000 into a savings account that earns 5%, compounded annually, for future generations of your family. How much will be in the account after 200 years? (See Example 2.)

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    __    __    ______  __    __     ___      ______  
\ \\ / //  /_   _// \ \\ / //   / _ \\   /_____// 
 \ \/ //    -| ||-   \ \/ //   | / \ ||  `____ `  
  \  //     _| ||_    \  //    | \_/ ||  /___//   
   \//     /_____//    \//      \___//   `__ `    
    `      `-----`      `       `---`    /_//     
                                         `-`
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  • 7. Investment by an Ancestor

    Suppose that 350 years ago, 1 of your ancestors deposited $1 into a savings account earning 6%, compounded annually. How much would be in the savings account today? (See Example 2.)

    • Worked-Out Solution

      Use the formula for compound interest.

      How is that possible? The point is that 6% annual interest is a high rate, especially during the past 350 years. During the first 250 of those years, the rate of inflation was low.

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      ______   __   __    _____    __   __   ______   
 /_   _//  \ \\/ //  /  ___||  \ \\/ // |      \\ 
 `-| |,-    \ ` //  | // __     \ ` //  |  --  // 
   | ||      | ||   | \\_\ ||    | ||   |  --  \\ 
   |_||      |_||    \____//     |_||   |______// 
   `-`'      `-`'     `---`      `-`'   `------`
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  • 8. Compounding a Penny

    Suppose that 500 years ago, the equivalent of 1 penny had been deposited into a savings account earning 8%, compounded annually. How much would be in the savings account today? (See Example 2.)

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     ______      ___      _____    _    _             
|      \\   / _ \\   / ____|| | || | ||     ___   
|  --  //  / //\ \\ / //---`' | || | ||    /   || 
|  --  \\ |  ___  ||\ \\___   | \\_/ ||   | [] || 
|______// |_||  |_|| \_____||  \____//     \__ || 
`------`  `-`   `-`   `----`    `---`       -|_|| 
                                             `-`
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