# 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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## Simple Interest

The amount of money borrowed or invested is the principal. The rate of interest is the percent of the principal charged for the use of the money. It is expressed as an annual rate, unless stated otherwise. The period of time for which the money is borrowed or invested may be expressed in years, months, or days, however, the unit of time must correspond to the rate. If the rate is given as an annual rate, the time must be expressed in terms of a year, that is, days or months must be converted to a fraction or multiple of a year. To calculate simple interest, multiply the principal by the rate of interest, then multiply that product by the time. The formula for finding simple interest states: Interest = Principal x Rate x Time.

Example 1: | Find the simple interest on $540 at 6% per year for 2 years. |

Solution: | Principal = $540 Rate = 6/100 Time 2 years |

Interest = $540/1 x 6/100 x 2/1 = $6480/100 | |

Interest = $64.80 | |

Example 2: | Find the simple interest on $980 at 12% per year for 10 months. |

Solution: | Principal = $980 Rate = 12/100 Time = 10/12 yr. |

____ ____ =980 /1 x 1/10 x 1/1= 980/10 = $98.00

Example 3: | Steve borrowed $1200 at 14% per year simple interest for 8 months. What was the total amount due when he repaid the loan? |

Solution: | Principal = $1200 Rate of Interest = 14/100 |

Time = 8/12 year | |

Interest = Principal x Rate x Time | |

Interest = $1200/1 x 14/100 x 8/12 = $112.00 | |

Amount Due = Principal + Interest | |

Amount Due = $1200 + $112 = $1312. |

- 1. Ordinary simple interest in which an “interest year” consists of 360 days or twelve months of thirty days each. The number of days used in computing ordinary simple interest is known as approximate time. This method is used frequently to compute interest on installment loan.
- 2. Banker’s or commercial interest in which an “interest year” consists of 360 days, but the exact number of days in the interest period are used. This method results in a greater return to the lender.
- 3. Accurate interest in which an “interest year” consists of 365 days, and the exact number of days in the interest period are used. This method is used by the federal government and some banks.

Example 1: | Find the approximate time and the exact time from June 12, 1980 to October 24, 1980. Exclude the first day, but include the last day. |

Approximate | Exact | |

Number | Number | |

Month | of Days | of Days |

June 12 30 | 18 | 18 |

July | 30 | 31 |

August | 30 | 31 |

September | 30 | 30 |

October | 24 | 24 |

Total | 132 days | 134 days |

Example 2: | Find the ordinary, banker’s and accurate interest on $1560 at 15% per year for a loan dated March 21 and due June 6 of the same year. | |

Solution: | Ordinary Interest | |

Principal = $1560 Rate = 15% Time 75 days | ||

Interest = 1560/1 x 15/100 x 75/360 | ||

= 39/1 x 5/4 = 195/4 = $48.75 | ||

Ordinary Interest = $48.75 | ||

Banker’s Interest | ||

Principal = $1560 Rate = 15% Time = 77 days | ||

Interest = 1560/1 x 15/100 x 77/360 | ||

= 13/1 x 77/20= 1001/20 = $50.05 | ||

Banker’s Interest =$50.05 | ||

Accurate Interest | ||

Principal = $1560 Rate = 15% Time = 77 days | ||

Interest = 1560/1 x 15/100 x 77/365 | ||

= 78/1 x 3/1 x 77/365 | ||

= 18018/365 =$49.364 = $49.36 | ||

Accurate Interest = $49.36 | ||

Example 3: | The banker’s simple interest paid on a sum of money invested at 8% per year for 90 days was $18. How much money was invested? | |

Solution: | Principal = N Rate 8% Time =90/360 year Principal x Rate x Time = Interest | |

N/1 x 8/100 x 90/360 = $18 | ||

720N/36000= 18/1 | ||

N/50 =18/1 | ||

N =$900 | ||

The amount invested was $900. |

- 1. Find the approximate time and exact time for the following: a) March 17, 1980 to July 8, 1980 b) September 3, 1979 to February 26, 1980.
- 2. Jack borrowed $5,000 to buy a car. He repaid the loan at the end of four years. The ordinary simple interest on $5,000 for 4 years was $300. What was the annual rate of interest?
- 4. Complete the table.

Annual | Simple | |||

Principal | Rate | Time | Interest | |

820 | 5% | 4 months | ||

1,350 | 7. | 5% | 5 years | |

$1 800 | 8% | 70 days | (ordinary) | |

12% | 10 months | $ 40 | ||

$1,500 | 2 years | $180 | ||

$2,400 | 5.25% | $504 | ||

$7,960 | 15% | 250 days | (exact) | |

$ 675 | 10% | 80 days | (banker’s) |

- 5. Bob invested $2,700 at 11% per year simple interest for 15 months. How much interest did he receive on the investment?
- 6. A man borrowed $500 on June 1 at 18% per year exact simple interest. He repaid the loan in full on the following August 30, What was the total amount repaid?