### 6.4 Savings & Retirement Plans

<
>
• 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.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  ______    _____      _____   _    _     ____
/_____//  |  ___||   / ___// | || | ||  |  _ \\
`____ `   | ||__     \___ \\ | || | ||  | |_| ||
/___//    | ||__     /    // | \\_/ ||  | .  //
`__ `     |_____||  /____//   \____//   |_|\_\\
/_//      `-----`  `-----`     `---`    `-` --`
`-`
```
• 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

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

```
• 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 has a greater balance after 15 years.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

``` _____      _____    __   __     ___      _____
|  __ \\   |  ___||  \ \\/ //   / _ \\   |__  //
| |  \ ||  | ||__     \   //   / //\ \\    / //
| |__/ ||  | ||__     / . \\  |  ___  ||  / //__
|_____//   |_____||  /_//\_\\ |_||  |_|| /_____||
-----`    `-----`   `-`  --` `-`   `-`  `-----`

```
• 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.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

``` _____     _    _     ______     ___     _    _
|  __ \\  | || | ||  /_   _//   / _ \\  | \  / ||
| |  \ || | || | ||    | ||    / //\ \\ |  \/  ||
| |__/ || | \\_/ ||   _| ||   |  ___  ||| .  . ||
|_____//   \____//   /__//    |_||  |_|||_|\/|_||
-----`     `---`    `--`     `-`   `-` `-`  `-`

```
• 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.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  _____      ___    __    __    ______     _____
/  ___||   / _ \\  \ \\ / //  /_   _//   / ___//
| // __    | / \ ||  \ \/ //    -| ||-    \___ \\
| \\_\ ||  | \_/ ||   \  //     _| ||_    /    //
\____//    \___//     \//     /_____//  /____//
`---`     `---`       `      `-----`  `-----`

```
• 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.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

``` _    _      ___               _    _    _    _
| || | ||   / _ \\    ____    | || | || | |  | ||
| || | ||  / //\ \\  |    \\  | || | || | |/\| ||
| \\_/ || |  ___  || | [] ||  | \\_/ || |  /\  ||
\____//  |_||  |_|| |  __//   \____//  |_// \_||
`---`   `-`   `-`  |_|`-`     `---`   `-`   `-`
`-`
```
• 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.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  ____       ___      _____      ___     __   _
|  _ \\    / _ \\   /  ___||   / _ \\  | || | ||
| |_| ||  | / \ || | // __    / //\ \\ | '--' ||
| .  //   | \_/ || | \\_\ || |  ___  ||| .--. ||
|_|\_\\    \___//   \____//  |_||  |_|||_|| |_||
`-` --`    `---`     `---`   `-`   `-` `-`  `-`

```
• 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.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
``` _____     __   __    _____    _    _    __   __