5-Minute Work-out for Future value and Present value of Annuities

Dr. P. Peterson

Future value of an ordinary annuity


Problem   Periodic cash   Number of    Rate per     Future value as    
          flow            cash flows   period       of the last cash   
                                                    flow               

1         $1,000          5            4%                              

2         $100            40           1%                              

3         $2,000          20           2%                              

4         $1,000          10           5%                              

5         $1,000          12           1%                              



Present value of an ordinary annuity


Problem   Periodic cash   Number of    Rate per     Present value of   
          flow            cash flows   period       cash flows         

1         $100            12           1%                              

2         $1,000          30           1%                              

3         $5,000          10           4%                              

4         $10,000         12           3%                              

5         $10,000         12           4%                              



Solutions to 5-Minute Work-outs

Future value and Present value of Annuities

Future value of an ordinary annuity


Problem  Periodic    Number of     Rate per       Future value   
         cash flow   cash flows    period         as of the      
                                                  last cash      
                                                  flow           

1        $1,000      5             4%             $5,416.32      

2        $100        40            1%             $4,888.64      

3        $2,000      20            2%             $48,594.74     

4        $1,000      10            5%             $12,577.89     

5        $1,000      12            1%             $12,682.50     



Present value of an ordinary annuity


Problem  Periodic    Number of     Rate per       Present value  
         cash flow   cash flows    period         of cash flows  

1        $100        12            1%             $1,125.51      

2        $1,000      30            1%             $25,807.71     

3        $5,000      10            4%             $40,554.48     

4        $10,000     12            3%             $99,540.04     

5        $10,000     12            4%             $93,850.74