1037  500  500  ...  500  800  800  ...  800 
      ...        ...   
0  1  2  ...  60  61  62  ...  84 
¯ 
balance = 1037(1+i)^{84}+500s_{60i}(1+i)^{24}800s_{24i} = $19711.22.
Her balance just after her last withdrawal is $19711.22.
...  7370  7370  7370  7370  
R  R  ...  R  
      ...         
0  1  2  ...  8  9  10  11 
¯ 
At time `8': Rs_{8.062}7370a_{4.062}(1.062) = 0 so R = 2708.19
Each of his deposits should be $2708.19.
700  700  ...  700  747  747  ...  747  
      ...        ...   
0  1  2  ...  4  5  6  ...  12 
¯ 
At time `1': 700a_{4i}(1+i)+747a_{8i}(1+i)^{3} = 8599.09
The amount needed on September 1, 1999 is $8599.09.
737  737  ...  737  ...  737  ...  737  
      ...    ...    ...   
0  1  2  ...  19  ...  27  ...  42 
  8%    7%    6%    
¯ 
At time `42': 737[s_{15.015} + (1.015)^{15}(s_{8.0175} + (1.0175)^{8} s_{19.02})] = 44312.86.
The balance October 1, 1999 is $44312.86.
For leasing, NPV = (PV of revenue)  (PV of cost) = (9370a_{60.0075})(8000a_{60.0075}(1.0075)) = $63107.12.
Thus buying is better and the savings is $13825.38. [Note: This is the same answer for all values of K because the machine monthly revenue cancels when you subtract.]
210000 = 1470a_{n.00658333} so (210000)(.00658333)/1470 = 1(1.00658333)^{n} and (1.00658333)^{n} = 16.8. Taking logs give n = (log 16.8)/(log 1.00658333) = 429.97
Thus 430 monthly payments are needed. (That's 35 years and 10 months.)
0.9L = (L/16)a_{16i} or cancelling the L, a_{16i} = 0.9(16) = 14.4. The approximate formula for i gives i » (1(14.4/16)^{2})/14.4 = 0.013194. This gives j_{12} » 15.8%. Taking j_{12} = 16% gives a_{16i} = 14.32301. To get a value larger than 14.4 we must reduce the interest rate. Taking j_{12} = 15% gives a_{16i} = 14.42029. Hence

Thus the equivalent rate charged by the store is j_{12} = 15.2086% [Note: All answers are the same since there was no K in this question.]
The mortgage requires 173 full payments of $1370 followed by a final 174th payment of $280.98.
Her monthly payment for 24 months is $8158.43. [Note: Answer independent of K.]
The amount of the court award is $367274.16.