606 CHAPTER 10 Consumer Mathematics To help us understand how compound interest works, we will consider an investment of $5000 that is invested in a 1-year certificate of deposit paying 3% interest compounded quarterly. We will determine the amount, A, to which the $5000 will grow in 1 year. We begin by computing the interest for the first quarter using the simple interest formula. Add this interest to the principal to determine the amount at the end of the first quarter. In our calculation, time is 1 4 of a year, or t 0.25. = i prt A $5000 0.03 0.25 $37.50 $5000 $37.50 $5037.50 = = × × = = + = Now repeat this process for the second quarter, this time using a principal of $5037.50. i A $5037.50 0.03 0.25 $37.78 $5037.50 $37.78 $5075.28 = × × ≈ = + = For the third quarter, use a principal of $5075.28. i A $5075.28 0.03 0.25 $38.06 $5075.28 $38.06 $5113.34 = × × ≈ = + = Definition: Compound Interest Interest that is computed on the principal and any accumulated interest is called compound interest. Compound Interest An investment is the use of money or capital for income or profit. We can divide investments into two classes: fixed investments and variable investments. In a fixed investment, the amount invested as principal may be guaranteed and the interest is computed at a fixed rate. Guaranteed means that the exact amount invested will be paid back together with any accumulated interest. Examples of a fixed investment are savings accounts, money market deposit accounts, and certificates of deposit. Another fixed investment is a government savings bond. In a variable investment, neither the principal nor the interest is guaranteed. Examples of variable investments are stocks, mutual funds, and commercial bonds. Simple interest, introduced earlier in the chapter, is calculated once for the period of a loan or investment using the formula i prt. = The interest paid on savings accounts at most banks is compound interest. A bank computes the interest periodically (for example, quarterly, monthly, or daily) and adds this interest to the original principal. The interest for the following period is computed by using the new principal (original principal plus interest). In effect, the bank is computing interest on interest, which is called compound interest. Why This Is Important Investments that involve compound interest may play an important role in reaching some of your long-term financial goals. For example, if you want to make a down payment on a house in 5 years, understanding compound interest will help you determine how much money you need to invest now so that you reach this goal.
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