### 6.4 Savings & Retirement Plans

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• Math Help

In Example 1, the formula for the account balance is for interest compounded monthly. In Example 2, however, the balances are calculated for interest compounded annually. The balance A in a savings account with a principal of P, for n years at an annual percentage rate of r (in decimal form), compounded annually, is

You can use this formula to find the account balances in Example 2 as shown.

1. After 100 years, Benjamin Franklin expected each account balance to have about \$584,449.

2. In 1991, the account balance for Boston was about \$5,559,976.

To obtain the estimate of what Franklin intended for both cities to have in 1991, first find 25% of the result of part (a).

Then use the formula , where P = \$146,112.25, r = 0.05, and n = 100, to find the amount for one city.

So, Franklin expected the account balance for one city to be about \$19,213,945 in 1991, or \$38,427,890 for both cities.

You can read Benjamin Franklin's last will and testament by visiting The Franklin Institute.

• Consumer Suggestion

Most people know that Benjamin Franklin was an inventor, but did you know that he was also responsible for popularizing the concept of "pay it forward?" Pay it forward implies that when a good deed is done for you, you must pay it forward by completing a good deed for someone else. To learn more about this concept you might want to check out the movie Pay it Forward, which stars Haley Joel Osment and Kevin Spacey.

• Checkpoint Solution

Using the graph on page 165, the CPI in 1790 appears to be about 10 and the CPI in 1991 appears to be about 140. So, the approximate value of \$5.6 million (1991) in 1790 dollars is

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