Answer to Question #128746 in Financial Math for Junaid Mahida

Question

Carl​ Hightop, a popular basketball​ player, has been offered a two​-year salary deal. He can either accept ​$2,300,000 now or accept monthly amounts of ​$100,000 payable at the end of each month. If money can be invested at 5.6​% compounded semi-annually​, which option is the better option for Carl and by how​ much?

The option is better by $?

Answer 1

at single payment salary 2,300,00 for 2 year at 5.6 % rate

C.I. = P [ (1+ r)^nt - 1)

for semi anually (n = 2)

C.I. = 2,300,000 [(1+0.056)^2*2 -1 )]

C.I. = 2,300,000 [(1.056)⁴ - 1]

C.I. = 2,300,000[1.24 - 1]

C.I. = 2,300,000 [ 0.24 ]

C.I. = 552,000

at monthly payment salary 100,000 for 2 years at 5.6%

total salary is (2 year = 24 months)

100,000 (24) = 2,400,000

now we calculate compound interest for payment

C.I. = P [(1+r)^nt - 1]

C.I. = 2,400,000[(1+0.056)^2*2 -1]

C.I. = 2,400,000 [ (1.056)⁴ -1]

C.I. = 2,400,00 [ 1.24 - 1]

C.I. = 2,400,000 (0.24)

C.I. = 576,000

Now we know single payment compound interest is less than the monthly compound interest after investment at 5.56%.

now how much :

C.I.(monthly at the end of each month) - C.I.(for at single payment)

= 576,000 - 552,000

= 24,000 $