# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.07

## Solving Problems “by the Hundreds” A Study of Percentage and Its Applications in the Study of Consumer Related Problems

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## Compound Interest Table

To calculate compound interest with pencil and paper for sums in excess of four or five interest periods is a very tedious and time consuming chore. Where computation are long, tables have been worked out to reduce the arithmetical processes to a minimum. The compound interest table below shows the amount to which one dollar grows when invested at compound interest, at a specified rate, and over a specified number of interest periods.

To what amount will each of the following increase? How much compound interest will each accumulate?

Using the table, compound interest may be found in the following way:

- 1. Divide the annual rate of interest by the number of interest periods in one year. The result is the rate of interest for each period.
- 2. Multiply the number of interest periods in one year by the number of years given in the problem. The result is the total number of interest periods to be used.
- 3. Read down under the column headed “interest periods” until you reach the total number of interest periods to be used. Follow this line across until you reach the column with the rate of interest found in step 1 for each period. The amount shown in this position in the table is the amount to which $1.00 has grown in the given number of years at the given percent.
- 4. Multiply this amount by the principal to obtain the total amount to which the principal has increased.
- 5. Compound Interest Total Amount Original Principal.

Example: | How much will $925 amount to in ten years at 6% per year compounded semiannually? What amount of compound interest will be accumulated? |

Solution: | 1. The rate of interest for one interest period is 6 Ö 2 =3%. |

2. The number of interest periods is 10 x 2 = 20. | |

3. In the compound interest table below, read down under the column headed “interest periods” to 20. Read across the line on which 20 appears to the column headed 3%. The amount shown is 1.8061. This means that $1.00 will increase to $1.8061 in ten years when compounded semiannually at 6%. | |

4. To find the amount to which $925 will increase, multiply $1.8061 by 925. $1.8061 x 925= $1670.6425 = $1670.64. | |

5. The compound interest earned is $1,670.64 $925.00 = $745.64. |

(figure available in print form)