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 Case Study: Mary Let's look at the example of an average person, Mary, who wants to have a comfortable sum set aside upon retirement. Mary is 30 years old and works for an insurance company. She makes \$340 per week. After expenses, she can afford to put \$60 per week aside for savings. Mary puts her \$60 per week into a savings account. The bank pays 6% interest each year on the money Mary deposits into her savings account. In fact, what the bank is doing is paying Mary for the use of the money she deposits, and the amount they are paying her is called interest. The amount that Mary deposits is called the principal and the 6% extra she earns while her money is in the bank is called the interest rate. Interest rates are always given for specific periods of time (one year is common). Each time that period of time elapses, the interest rate is applied. In Mary's case, at the end of the first year, a sum equal to 6% of what she deposited will be added to her account. This is called simple interest. It's simple because it computes only the interest earned for a fixed period of time (such as one year). It does not compute the interest you'd earn on interest—or what is called compound interest, which we'll look at in a moment. How much will Mary have at the end of one year? Remember, Mary's money earns 6% each year she keeps it in the savings account. How much total interest will it earn in the first year? There's a mathematical formula that can help us find the answer: I = Prt In this formula, we're multiplying the amount of Mary's deposit by the interest rate and the number of years she keeps her money in the bank. Interest (I) equals principal (P) multiplied by the rate of interest (r) and the time in years (t). To learn the amount Mary's money will earn the first year, these are the numbers we plug into the formula: Principal = \$3,120 (\$60 per week x 52 weeks) Rate of interest = .06 (6%) Time in years = 1 year If we plug these numbers into the formula we get: \$3120 x .06 x 1 = \$187.20 At the end of the first year, Mary's money will have earned \$187.20 in interest. She now has more than the \$3,120 she deposited. Her total saved at the end of the first year: \$3,307.20. How much more can Mary earn by continuing to save? Obviously, Mary wants her money to work for her for much longer than one year. In fact, she'll be putting her money to work for 35 years, until she is ready to retire. After the first year, Mary will continue to deposit \$3,120 into her savings account each year. When it's time to compute the 6% interest Mary has earned at the end of the second year, Mary will have earned interest on more than just the original \$3,120 she deposited. She'll also have earned interest on the additional \$3,120 she added to the account in the second year. And she'll even have earned interest on the first year's interest of \$187.20. At the end of the second year, Mary will have earned \$385.63 in interest. That's 6% of the \$6,427.20 she has in the bank at the end of the second year. As Mary goes into her second year with the savings account, her interest changes from simple interest to compound interest. She's now earning interest on the interest she's earned, as well as earning interest on the principal. By continuing to deposit \$3,120 per year and earning an interest rate of 6% annually, how much will Mary have when she retires? You might be surprised. Mary will retire with \$368,537.10 in her savings account. She only deposited \$109,200 over the course of 35 years, but her money earned her an additional \$259,337.10 in interest. Try it yourself. Calculate compound interest on your own savings.
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