The Mathematics of Money

158 Chapter 4 Annuities

b. Bucket

Payment from Year Payment Amount Years of Interest Future Value

1 $1,359.55

2 $1,359.55

3 $1,359.55

4 $1,359.55

Grand total

B. Finding Future Values by Using Annuity Factors (Ordinary Annuities, Annual Payments)

Exercises 2 and 3 are intended only for those evaluating annuity factors by using the formulas.

2. 
   

   Calculate s __ 48 | (^) 0.0042 as follows.
   a. Write the annuity factor formula, plugging in the appropriate values for n and i.
   b. Evaluate the formula by following the calculator steps shown below and fi lling in the values in the Result column of
   the table below.
   Operation Result
   (1.0042)^48
   
    1
   
   /.0042
   

   
   


3. 
   

   Calculate s __ 54 | (^) .065 as follows
   a. Write the annuity factor formula, plugging in the appropriate values for n and i.
   b. Evaluate the formula by following the calculator steps shown below and fi lling in the values in the Result column of
   the table below.
   Operation Result
   (1.065)^54
   
    1
   
   /.065
   
   To fi nd the annuity factors for these problems, use whatever method your instructor is requiring you to use in the course you
   are taking. Depending on the precision of your calculator (or table) your answers may have more or fewer decimal places
   than the “back of the book“ answers.

   
   


4. 
   

   Calculate s _n|i if n
   24 and i
   .015.

   
   


5. 
   

   a. Calculate s _n| (^) i if n
   20 and i
   .095.
   b. Use your answer from (a) to fi nd the future value of $1,000 invested at the end of each year for 20 years, assuming
   a 9.5% interest rate.

   
   


6. 
   

   a. Calculate s _ 4 | (^) 0.057.
   b. Use your answer from (a) to fi nd the future value of the annuity from Problem 1.