Question

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.

Answer 1

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