Simple Interest

• This is the most basic of loans.
• You borrow some money for a fixed period of time at a fixed interest rate, and pay it off in a single payment.
• Terms:
  • The money you borrow is called the principal.
  • The period of time you borrow the money for is called time.
  • The interest rate (expressed as a %) is the rate
  • The "rent" you owe on the money is called interest.
• The relationship between these is i=prt
• The amount you owe in the end is the principal plus the interest.
• Interest rates, unless stated otherwise are in terms of annual percentage rate.
• Everything must be in terms of the same period (usually years)
• Bankers assume that 1 year= 360 days.
• Examples:

  Question 2 page 448
      P = $7000, r = 5%, t = 1 year
      i = prt
      i = $7000 * .05 * 1 = 350
  Question 4
      P = $260, r = 4%, t - 2 years
      i = prt
      i = 260*.04*2 = 48.8
  Question 6
      P = 18,000 r = 7.5, t = 18 months.
      12 months = 1 year.
      18 months x 1 year/12 months = 1.5 years
      i = prt 
      i = 18000 * .075 * 1.5 = 2,025
  Question 8
      P = $12,600, r = 9%, t = 60 days.
      350 days = 1 year
      60 days * 1 year/350 days = .17 year
      i = prt
      i = 12,600 * .08 * .17 = 192.78
      

• The future value of a loan is the amount you need to pay in the end.

  A = p + i    i = prt
  A = p + prt
  A = p(1+rt)
      

• Example:

  Problem 10
     P = $2000, r = 6%, t = 3 years
     A = p(1+rt)
     A = 2000*(1+.06*3) = $2,360
  
      

• Sometimes we need to do a little algebra.
• Example:

  Problem 16, given P, A and t,  find r
      A = P(1+rt)
      A = P+ Prt
      A-P = Prt
      (A-P)/Pt = r
      P = $3000, A = 3180, t = 1
      (3180-3000)/(3000) = .06 or 6%
  Problem 22, given A r and t find P
      A = P(1+rt)
      A/(1+rt) = P
      A = 8500, r = 7%, t = 3 years
      8500/(1+.07*3) = 7,024.79
      

• A discount loan is just a bit strange.
  • The amount you are credited for is the principal + interest.
  • The loan's discount is the interest paid.
  • The net amount is the amount - discount
  • The actual interest rate is calculated on these amounts.

    Number 30,
       You borrow $20,000 on an 8.5% discount loan for a period of 3 years.
       1. Find the discount rate.
          i = prt
          i = 20,000 * 8.5 * 3 = 5,100
       2. Find the money received:
          20,000 - 5,100 =  14,900
       3. Find the actual interest rate.
          i = prt
          r = i/pt
          r = 5,100/(14,900*3) = 11.4%
    	

Homework: