# 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

To calculate compound interest, divide the annual rate of interest by the number of interest periods in the year. Multiply the result by the principal to obtain the interest for the period. Add this amount to the principal to find the new principal at the beginning of the next

interest period. Repeat this procedure for the desired number of interest periods. The difference between the final amount and the original principal is the compound interest accumulated.

Example: | John invested $500 at 6% compounded monthly. How much compound interest did he earn during the tour months? |

Solution: | Monthly rate of interest is 6% 12 .5% |

Balance at | Balance at | ||||

Beginning | End of | ||||

Month | of Month | Interest | Month | ||

1 | $500.00 | .5/100500/12.50 | $502.50 | ||

2 | $502.50 | .5/100 x 502.50/1 | = 2.51 | $505.01 | |

3 | $505.01 | .5/100 x 505.01/1 | = 2.53 | $507.54 | |

4 | $507.54 | .5/100 x 507.54/1 | = 2.54 | $510.08 |

Solve the following set of problems.

- 1. How many interest periods are there in six years if interest is compounded and paid annually? Quarterly? Semiannually? If the interest rate is 10% per year, what is the interest rate per period of time for each of these interest periods?
- 2. If a person deposits $500 in a savings account, how much will he have at the end of two years if the interest is compounded semiannually at 5.5% per year? ‘What amount of compound interest will he earn?
- 3. Mary invested $2,500 at 8% interest per year compounded quarterly. How much did she have at end of 1 1/2 years? How much compound interest did she receive?
- 4. How much more compound interest will $850 earn at 6.5% compounded quarterly as compared to semiannually at the rate of 14% per year?