Question

As a new employee in the Lottery Commission, your first job is to design a new prize. Your idea is to create two grand prize choices: (1) receiving the lump sum of $1 million at the end of year 5, or (2) receiving $500,000 today followed by a lump sum amount at the end of year five. Using an interest rate of 8%, which of the following comes closest to the amount prize (2) needs to pay at the end of year five in order for both prizes to have the same present value?

a.
$265,336
b.
$333,333
c.
$500,000
d.
$680,580
e.
$1,000,000

Answer 1

a. $265,336

Step-by-step explanation:

we are told to calculate which amount will make both payments equal:

• payment 1 = $1,000,000 in 5 years
• payment 2 = $500,000 now + ? in 5 years

in order to be able to compare them, we must determine the value of the $500,000 paid now in 5 years:

future value = present value x (1 + interest rate)ⁿ

future value = $500,000 x (1 + 0.08)⁵ = $734,664

$1,000,000 = $734,664 + ?

? = $1,000,000 - $734,664 = $265,336