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Question

Two tennis superstars, Novak and Maria were offered contracts from a company to advertise a product. The company offered Novak 150 thousand dollar signing bonus and a five-year contract promising him 400 thousand dollars for the first year and an increase of 3% per year over the next 4 years. The contract offered to Maria was just 450 thousand dollars per year over the same five-year period. Both Novak and Maria keep their savings at the same bank which provides interest rate of 4% compounded continuously. If money is transferred continuously to the bank accounts, which offer was more attractive? Why? Provide your calculations!?

Answer 1

Novak:

 

     year 0:    150 k

 

    year 1:   150 k increases by  4% = 156k <--- the signing bonus accumulates interest

                  156k + 400 k = 556k <-- 1st year is 400k

 

    year 2:  556k increases by 4%  =    578.24

                 400 k increases by 3% = 412k

              578.24 + 412  = 990.24

 

  year 3 :  990.24 increases by 4% = 1029.8496

                412 increases by 3% = 424.36

               1029.8496 + 424.36 = 1454.2096

 

year 4:  1454.2096 increases by 4% = 1512.377984

             424.36 increases by 3% = 437.0908

            1512.377984 + 437.0908 = 1949.468784

 

year 5: 1949.468784 increases by 4% = 2027.44753536

          437.0908 * 1.03 = 450.203524

          2027.44753536 + 450.203524 = 2477.65105936

 

          $2, 477, 651.06

 

 

Maria:

 

  year 0:  0

  year 1: 450 k

 

  year 2: 450 k increases by 4% = 468k

              468 k +450 k = 918k

 

 

 year 3:  918 k increases by 4% = 954.72

             954.72 +450  = 1404.72

 

year 4:  1404.72 increases by 4% = 1460.9088

             1460.9088 + 450 = 1910.9088

 

year 5: 1910.9088 increases by 4% = 1987.345152

            1987.345152 + 450 = 2437.345152

 

 $2,437,345.15

 

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$2, 477, 651.06 - 2,437,345.15 = 40305.91