Linus has just won the "Wait To Spend" lottery. SpecificallyLinus has won the lump sum...

Linus has just won the "Wait To Spend" lottery. Specifically Linus has won the lump sum amount of $1250 but he must wait until the end of 8 years to receive the money. Linus is in need of cash and would rather receive a different pattern of payments: $375 today and then receive some unknown LUMP SUM (i.e. one time) amount that will be received in 8 years. Using an interest rate of14.50%, determine the unknown lump sum amount that would make the present value of both prizes equivalent.

Solutions

Expert Solution

Option 1

To receive $ 1250 at the end of 8 years.

Present value of this option can be calculated with help of below formula-

PV = 1250 / ( 1 + 0.1450)⁸

= 1250 (1.1450)⁸

= 423.1224996

= 423.12 $ (approx)

Option 2

To receive $375 today and then receive some unknown LUMP SUM in 8 years.

In order to receive 375 $ today, rest lump sum amount will be future value of $ 48.12 (423.12 - 375 ) that will be received in 8 years to make the present value of both the options equal.

FV = PV (1 + r)ⁿ

FV = 48.12 ( 1 + 0.1450)⁸

= 48.12 (1.1450)⁸

= 142.1574132

= 142.16 $ (approx)

Unknown lump sum amount that would make the present value of both prizes equivalent = $ 142.16

jeff jeffy answered 2 years ago

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