Let’s compare different final values of a loan at the end of one year as we increase the number of times we compound the interest throughout the year.
Consider annual interest on a loan at the end of one year. Remember has a decimal equivalent of so the associated growth factor is
Compounded annually (one big piece), the loan value is
Compounded monthly ( pieces in a year), the loan value is
Compounded weekly.
- How many weeks are in a year? weeks in a year.
- The annual interest is divided into equal sized pieces and the small interest is calculated each week. What is the weekly interest percentage?
Approximately each week. (round to decimal places)
- What is the growth factor associated with the weekly percent increase? (Remember to use the decimal equivalent of the weekly percent!)
. (round your answer to decimal places)
- At this point we need a reminder for using calculators to get the most accurate results. Rule 1: Do not round any values until the final answer. Rule 2: Enter your calculations in one step.
For example, the value of the loan compounded monthly was calculated using the expression The entire expression on the left of the equation is entered into the calculator in one step, then press Enter only once. The final answer is the only time rounding occurs.
Not following these instructions will result in wrong answers.
Calculate the value of the loan using the weekly growth factor for the period of the entire year.
Loan Value (round to the nearest cent)
- Complete the table below for various values of the number of of times the interest is compounded during the year, and the value of the loan in dollars after one year.(round the money values to the nearest cent)