finance.8-25-98 - Finance 1.1 1.1 Simple Interest Simple...

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Finance 1.1 Simple Interest 1.1 Simple Interest Interest is money that is paid from one party to another for the privilege of having borrowed an initial sum of money called, the principal . At first, this definition of interest may seem to apply only to loans, but when you deposit money in a bank account, for instance, you have effectively loaned money to the bank, so the bank pays you interest rather than you paying the bank. For the sake of simplicity, we will adopt the vantage point that interest is being earned (as opposed to owed) on principal and we will distinguish between loans, accounts and investments only in the examples and as necessary. There are many ways to compute interest, but the most basic one, on which many other types of interest are based, is simple interest . The idea behind simple interest is that the amount of interest earned on an account is directly proportional to the length of time that the principal was deposited. For instance, the amount of interest earned on a simple interest savings account after two years should be twice the interest earned after only one year. This suggests the following formula for calculating the total amount of simple interest earned: (interest) = (amount of principal) (interest rate) (length of time) Let us establish some notation so we can formalize this relation. I = interest P = principal r = interest rate (in decimal form) 1 t = time (in years) Then, in symbols, what we have said is that, Simple Interest Formula I = Prt When working with the formula I = Prt , remember that r should be in decimal form. 1 Unless otherwise stated, all interest rates will be annual percentage rates (APR). 1-1
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Finance 1.1 Simple Interest Tip: Converting percents to decimal forms: To convert a percentage to decimal form, move the decimal point two places to the left. For instance, 9.2% r = .092, while 13% r = .13. Also, all time intervals should be converted to years. For instance, 37 months t = 37 12 years (there are 12 months in a year) 19 weeks t = 19 52 years (there are 52 weeks in a year) 281 days t = 281 365 years (there are 365 days in a year) Example 1: Joan borrows $1500 for 15 months at the simple interest rate of 12.0%. How much interest will she have to pay at the end of the 15 month period? Solution: Since we wish to calculate the total amount of interest due on a simple interest loan, we use the formula I = Prt . The principal, P , is the amount borrowed, so we set P = 1500. The interest rate 12.0% is converted to r = 0.12 and the time, given in months, is converted to 15/12 years. Thus, I = Prt 12 15 ) 12 . 0 )( 1500 ( I I = $225.00 Keystrokes: 1500 0.12 15 12 ENTER Joan will have to pay $225.00 in interest. The primary use of the formula I = Prt is to compute the value of I by plugging in values for P , r and t . However, given any three of the four variables, we can always solve for the fourth. In the next example, the values of I , r and t are given and the value of P is sought.
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