6.6  Computing Interest              

 

Simple Interest (no compounding)

 

          I = Prt                   P-principal      r-Interest rate           t-time

 

Total With Interest              A = P + I = P + Prt = P(1 + rt)

 

If a person borrows $150 at 4% annual interest rate,

          a)  If pay off in 1 year, what is the simple interest? 

 

     How much total is due?

 

 

          b)  If pay off in 90 days, what is the simple interest? 

 

               How much total is due?

 

          c)  If pay off in 18 months, what is the simple interest? 

 

              How much total is due?

 

 

 

A man collected $28,500 on a loan of $25,000 he made 4 years ago.  If he charged simple interest, what was the rate he charged?

 

 

 

 

 

 

Compound Interest            Interest is computed on previous interest

 

“annually”         “semiannually”       “Quarterly”       “Monthly”       “Daily”

 

         


For an annual interest rate of 4.5%, what is the “interest rate per period” if compounded:

 

          a)  annually

         

b)  semiannually

 

          c)  quarterly

 

          d)  monthly

 

          e)  daily

 

 

         

 

Consider  $2500,   8%,   5 years   find value after 5 years if:

 

a)  Compounded annually

 

 

 

b)  Compounded quarterly

 

 

 

c)  Compounded monthly

 

 

 

d)  Compounded daily

 

 

 

 

The Text uses the following version of the compounding formula:

                  

 

 

 

If borrow $1000 dollars for 2 years at 5% compounded quarterly

 

 

 

 

 

 

 

 

 

Prev. Balance

Interest

New Balance

 

vs Simple Interest

1

$1,000

$12.50

$1,012.50

 

Interest

100

2

$1,012.50

$12.66

$1,025.16

 

Total

1100

3

$1,025.16

$12.81

$1,037.97

 

 

 

4

$1,037.97

$12.97

$1,050.95

 

 

 

5

$1,050.95

$13.14

$1,064.08

 

 

 

6

$1,064.08

$13.30

$1,077.38

 

 

 

7

$1,077.38

$13.47

$1,090.85

 

 

 

8

$1,090.85

$13.64

$1,104.49

 

 

 

 

Burger Queen will need $50,000 in 5 years for a new addition.  To meet this goal, the company deposits money in an account today that pays 9% annual interest compounded quarterly.  Find the amount that should be invested to total $50,000 in 5 years.

 

 

 

 

 

 

 

 

 

 

Determine the number of years (to the nearest tenth) it would take for any amount of money to double if it were deposited at a 10% interest rate compounded annually.

 

 

 

 

 

 

 

 

Each year a car’s value depreciated 20% from the previous year.  Mike claims that after 5 years the car would depreciate 100% and would not be worth anything.  Is Mike correct?  Explain why or why not.  If not, find the actual percent the car would depreciate after 5 years.

 

 

 

 

 

 

 

 

 

 

 

“Effective” annual rate

If pay 3.5% compounded quarterly, what is effective annual rate?

 

     Assume $100 invested at 3.5% quarterly for one year,

     so effective annual yield is 3.546%

 

If have $825 in an account has been left alone for 3 years compounding annually at, what was the original amount?

 

  Use Algebra:   

 

Find Doubling Time    -  If put $2500 into an account, how long does it take to double at each of the following rates?

 

  5% compounded annually                            4% compounded daily