Compound interest formula nt

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					                                            r
Compound interest formula: A = A0 ( 1 + n )nt

A is the new value of the investment
A0 is the original amount of the investment
r is the annual interest rate, written as a decimal
n is the number of times the interest is compounded in a year
And t is the length of the investment, in years

Steps: 1) Write down the formula

       2) Fill in the missing amounts
                Determine the growth rate (______________ ÷ ____________________)

               Substitute the values for the original amount, the number of times
               compounded, and the time (in years)

       3) Calculate


Sample Problems: Find the value of $3200 invested for 3 years at 6.0% if the interest is
compounded
      a) quarterly

       b) semi-annually

       c) monthly

Solutions
a) A0 = 3200, r = .06, and t = 3. Since the interest is compounded quarterly, n = 4.
This gives us




b) A0 = 3200, r = .06, and t = 3. Since the interest is compounded semi-annually, n = 2.
This gives us
c) A0 = 3200, r = .06, and t = 3. Since the interest is compounded monthly, n = 12.




                                                            r
y = C(1 + r)t           y = C(1 – r)t           A  A 0 (1  ) nt
                                                            n


1. Mr. Stangeland invested $1500 in a fund that earns 4%. How much will this
investment be worth in 6 years if the interest is compounded:
       a) Quarterly




        b) Monthly




2. The town of Algebraville has an inflation rate of 3½ percent. An item today costs $150.

        a) What did it cost 3 years ago? (t = ____)




        b) What will it cost when Mr. Stangeland turns 50? (He is currently 35.)
3. Algebra-man is currently taking medication (prescribed) that keeps his brain from
getting too big. The amount of medication in his bloodstream dissipates at a rate of 20%
per hour. At 12:30 p.m., there is approximately 726 mg of the medication in his system.

           a) How much was in his system at 9:15 a.m., when he originally took the
              medication? (t = ______)




           b) How much will remain in his system at 3:15 p.m.? (t = _______)




4. The point (3, 2) is on the graph of y = a • 2x . What is the value of the y-coordinate
when x = 6.




5. (3xy3)4                      6. (ab2c3)–3(a4b3c)4                7. (2m)–5




                                                                                2
                                       3   3
                                                                           3 
                                                                          
      –2                              
                                      
                                      
                                      2x   
                                            
                                            
                                                                         
                                                                          4w 
                                                                               
8. 8x                           9.     2
                                      
                                      
                                            
                                            
                                            
                                                                    10.   
                                                                           2 
                                                                              
                                                                               
                                      
                                      3y   
                                                                         
                                                                          5y 
                                                                        
                                                                              
                                                                               




        1
         5 
              6
            
         x y  3 
                     2
11.         
              16xy 
                    
        
            
                   
        
        4   
             



BONUS: What is the ones digit of 22007? (Show your steps and/or explain your answer.)