11.2 Personal Loans and Simple Interest

• A loan is equivalent to "renting money".
• The principal is the amount of money that is given to the borrower.
• The interest is the amount of "rent" the borrower must pay in addition to the principal when repaying the loan.
• The interest is normally determined by an interest rate or simply rate
  • Unless otherwise stated, interest rates are given as annual percentages.
  • A month has 30 days
  • A year has 360 days
  • A year has 12 months.
• Some loans are given for a fixed period of time.
• We will study a number of loans, but the simple interest loan is the simplest.
  • There are not that many opportunities for simple interest loans.
  • But they form the foundation of other loans.
• i = prt
  • i = interest due
  • p = principal
  • r = rate
  • t = time
  • Note: time and rate must be in the same period
• Some examples:
  • Determine the simple interest.
    • p = $430, r = 7.2%, t = 2 years
    • p = $1230, r = 3.24, t = 30 days
    • p = $1000, r = 3 1/2% , t = 9 months.
    • p = $1234, r = 1.35% per month, 2 months.
  • Find the missing value
    • p = $1000, t = 2 years, i = $98
    • r = 7%, t = 6 months, i = $42
    • p = $500, t = 4%, i = $50
  • A man uses a loan program to obtain a loan for a business. HE borrows $30,000 for 4 years at a simple interest rate of 1.5%. How much must he repay after 4 years.
  • Problem 32 page 619
• If the question involves the word "discount" referring to the loan or the interest rate the loan is different.
  • Treasury bills, and savings bonds are this type of loan.
  • The amount of the loan stated in terms of interest plus principal.
    1. Compute the interest using i =prt
       • Use the amount for p
       • Use the discount rate for r
    2. Compute the actual principal (p)
    3. Compute the actual interest rate (r).
• Problem 28 page 619